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Deck 6: Section 2: Differential Equations
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Question
Find the exponential function 
that passes through the two given points. Round your values of C and k to four decimal places. 
A)
B)
C)
D)
E)
that passes through the two given points. Round your values of C and k to four decimal places. A)
B)
C)
D)
E)
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
The isotope 
has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.
A) 2.1332 , 2.0727
B) 2.7731 , 2.6945
C) 1.2799 , 1.2436
D) 1.7065 , 1.6582
E) 1.0666 , 1.0364
has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.A) 2.1332 , 2.0727
B) 2.7731 , 2.6945
C) 1.2799 , 1.2436
D) 1.7065 , 1.6582
E) 1.0666 , 1.0364
Question
Find the function 
passing through the point 
with the first derivative 
.
A)
B)
C)
D)
E)
passing through the point with the first derivative .A)
B)
C)
D)
E)
Question
The rate of change of N is proportional to N. When 
and when 
. What is the value of N when 
? Round your answer to three decimal places.
A) 2,129.520
B) 2,099.520
C) 2,049.520
D) 491.383
E) 262,440.000
and when . What is the value of N when ? Round your answer to three decimal places.A) 2,129.520
B) 2,099.520
C) 2,049.520
D) 491.383
E) 262,440.000
Question
The initial investment in a savings account in which interest is compounded continuously is $604. If the time required to double the amount is 
years, what is the amount after 15 years? Round your answer to the nearest cent.
A) $1,917.58
B) $1,804.46
C) $1,907.37
D) $1,404.46
E) $8,278.18
years, what is the amount after 15 years? Round your answer to the nearest cent.A) $1,917.58
B) $1,804.46
C) $1,907.37
D) $1,404.46
E) $8,278.18
Question
The isotope 
has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.
A) 7.2469 gm, 4.1988 gm
B) 6.2117 gm, 3.5989 gm
C) 10.3528 gm, 5.9982 gm
D) 4.1411 gm, 2.3993 gm
E) 12.4233 gm, 7.1979 gm
has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.A) 7.2469 gm, 4.1988 gm
B) 6.2117 gm, 3.5989 gm
C) 10.3528 gm, 5.9982 gm
D) 4.1411 gm, 2.3993 gm
E) 12.4233 gm, 7.1979 gm
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Question
Write and solve the differential equation that models the following verbal statement: The rate of change of 
with respect to 
is proportional to 
.
A)
B)
C)
D)
E)
with respect to is proportional to .A)
B)
C)
D)
E)
Question
Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: The rate of change of 
is proportional to 
. When 
, 
and when 
, 
= 84. What is the value of 
when 
?
A)
B)
C)
D)
E)
is proportional to . When , and when , = 84. What is the value of when ?A)
B)
C)
D)
E)
Question
Find the function 
passing through the point 
with the first derivative 
.
A)
B)
C)
D)
E)
passing through the point with the first derivative .A)
B)
C)
D)
E)
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The isotope 
has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 1.2 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal places.
A) 1.0706 , 0.0947
B) 2.4471 , 0.2164
C) 1.5294 , 0.1352
D) 2.1412 , 0.1893
E) 1.9883 , 0.1758
has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 1.2 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal places.A) 1.0706 , 0.0947
B) 2.4471 , 0.2164
C) 1.5294 , 0.1352
D) 2.1412 , 0.1893
E) 1.9883 , 0.1758
Question
The initial investment in a savings account in which interest is compounded continuously is $813. If the time required to double the amount is 
years, what is the annual rate? Round your answer to two decimal places.
A) 7.49 %
B) 7.70 %
C) 13.34 %
D) 6.29 %
E) 8.89 %
years, what is the annual rate? Round your answer to two decimal places.A) 7.49 %
B) 7.70 %
C) 13.34 %
D) 6.29 %
E) 8.89 %
Question
Question
The number of bacteria in a culture is increasing according to the law of exponential growth. After 5 hours there are 175 bacteria in the culture and after 10 hours there are 425 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. (i) Find the initial population.
(ii) Write an exponential growth model for the bacteria population. Let t represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000?
A) (i) 72.0588 ; (ii)
; (iii) 3,819.3668 ; (iv) 32.4162 hr
B) (i) 74.2088 ; (ii)
; (iii) 5,194.0840 ; (iv) 34.6442 hr
C) (i) 72.0588 ; (ii)
; (iii) 2,506.6327 ; (iv) 30.0817 hr
D) (i) 77.8388 ; (ii)
; (iii) 7,945.5374 ; (iv) 36.7554 hr
E) (i) 79.3988 ; (ii)
; (iii) 10,598.0009 ; (iv) 38.5348 hr
(ii) Write an exponential growth model for the bacteria population. Let t represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000?
A) (i) 72.0588 ; (ii)
; (iii) 3,819.3668 ; (iv) 32.4162 hrB) (i) 74.2088 ; (ii)
; (iii) 5,194.0840 ; (iv) 34.6442 hrC) (i) 72.0588 ; (ii)
; (iii) 2,506.6327 ; (iv) 30.0817 hrD) (i) 77.8388 ; (ii)
; (iii) 7,945.5374 ; (iv) 36.7554 hrE) (i) 79.3988 ; (ii)
; (iii) 10,598.0009 ; (iv) 38.5348 hr Question
Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is 0.024. Find the exponential growth model 
for the population by letting 
correspond to 2000. Round your answer to four decimal places.
A)
B)
C)
D)
E)
for the population by letting correspond to 2000. Round your answer to four decimal places.A)
B)
C)
D)
E)
Question
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 
. The initial temperature of the liquid is 
. After 3 minutes, the liquid's temperature is 
. How much longer will it take for its temperature to decrease to 
? Round your answer to two decimal places.
A) 1.89 minutes
B) 2.84 minutes
C) 3.16 minutes
D) 1.26 minutes
E) 3.47 minutes
. The initial temperature of the liquid is . After 3 minutes, the liquid's temperature is . How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places.A) 1.89 minutes
B) 2.84 minutes
C) 3.16 minutes
D) 1.26 minutes
E) 3.47 minutes
Question
Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected continuous annual rate of change of the population is 0.017. The exponential growth model for the population by letting 
corresponds to 2000 is 
. Use the model to predict the population of the country in 2013. Round your answer to two decimal places.
A) 83.08 million
B) 87.42 million
C) 90.45 million
D) 88.92 million
E) 81.68 million
corresponds to 2000 is . Use the model to predict the population of the country in 2013. Round your answer to two decimal places.A) 83.08 million
B) 87.42 million
C) 90.45 million
D) 88.92 million
E) 81.68 million
Question
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Deck 6: Section 2: Differential Equations
1
Find the exponential function that passes through the two given points. Round your values of C and k to four decimal places.
A)
B)
C)
D)
E)
that passes through the two given points. Round your values of C and k to four decimal places. A)
B)
C)
D)
E)
2
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
The half-life of the radium isotope Ra-226 is approximately 1,599 years. What percent of a given amount remains after 800 years? Round your answer to two decimal places.
A) 70.70 %
B) 5.71 %
C) 72.70 %
D) 25.02 %
E) 0.71 %
A) 70.70 %
B) 5.71 %
C) 72.70 %
D) 25.02 %
E) 0.71 %
70.70 %
4
The isotope has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.
A) 2.1332 , 2.0727
B) 2.7731 , 2.6945
C) 1.2799 , 1.2436
D) 1.7065 , 1.6582
E) 1.0666 , 1.0364
has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.A) 2.1332 , 2.0727
B) 2.7731 , 2.6945
C) 1.2799 , 1.2436
D) 1.7065 , 1.6582
E) 1.0666 , 1.0364
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5
Find the function passing through the point with the first derivative .
A)
B)
C)
D)
E)
passing through the point with the first derivative .A)
B)
C)
D)
E)
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6
The rate of change of N is proportional to N. When and when . What is the value of N when ? Round your answer to three decimal places.
A) 2,129.520
B) 2,099.520
C) 2,049.520
D) 491.383
E) 262,440.000
and when . What is the value of N when ? Round your answer to three decimal places.A) 2,129.520
B) 2,099.520
C) 2,049.520
D) 491.383
E) 262,440.000
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7
The initial investment in a savings account in which interest is compounded continuously is $604. If the time required to double the amount is years, what is the amount after 15 years? Round your answer to the nearest cent.
A) $1,917.58
B) $1,804.46
C) $1,907.37
D) $1,404.46
E) $8,278.18
years, what is the amount after 15 years? Round your answer to the nearest cent.A) $1,917.58
B) $1,804.46
C) $1,907.37
D) $1,404.46
E) $8,278.18
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k this deck
8
The isotope has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.
A) 7.2469 gm, 4.1988 gm
B) 6.2117 gm, 3.5989 gm
C) 10.3528 gm, 5.9982 gm
D) 4.1411 gm, 2.3993 gm
E) 12.4233 gm, 7.1979 gm
has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.A) 7.2469 gm, 4.1988 gm
B) 6.2117 gm, 3.5989 gm
C) 10.3528 gm, 5.9982 gm
D) 4.1411 gm, 2.3993 gm
E) 12.4233 gm, 7.1979 gm
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9
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
The half-life of the radium isotope Ra-226 is approximately 1,599 years. If the initial quantity of the isotope is 38 g, what is the amount left after 1,000 years? Round your answer to two decimal places.
A) 24.63 g
B) 30.60 g
C) 25.13 g
D) 11.88 g
E) 12.32 g
A) 24.63 g
B) 30.60 g
C) 25.13 g
D) 11.88 g
E) 12.32 g
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12
The half life of the radium isotope Ra-226 is approximately 1,599 years. If the amount left after 1,000 years is 1.8 g, what is the amount after 2000 years? Round your answer to three decimal places.
A) 1.167 g
B) 0.939 g
C) 1.800 g
D) 0.490 g
E) 2.334 g
A) 1.167 g
B) 0.939 g
C) 1.800 g
D) 0.490 g
E) 2.334 g
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13
Write and solve the differential equation that models the following verbal statement: The rate of change of with respect to is proportional to .
A)
B)
C)
D)
E)
with respect to is proportional to .A)
B)
C)
D)
E)
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14
Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: The rate of change of is proportional to . When , and when , = 84. What is the value of when ?
A)
B)
C)
D)
E)
is proportional to . When , and when , = 84. What is the value of when ?A)
B)
C)
D)
E)
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15
Find the function passing through the point with the first derivative .
A)
B)
C)
D)
E)
passing through the point with the first derivative .A)
B)
C)
D)
E)
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16
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Solve the differential equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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18
The isotope has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 1.2 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal places.
A) 1.0706 , 0.0947
B) 2.4471 , 0.2164
C) 1.5294 , 0.1352
D) 2.1412 , 0.1893
E) 1.9883 , 0.1758
has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 1.2 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal places.A) 1.0706 , 0.0947
B) 2.4471 , 0.2164
C) 1.5294 , 0.1352
D) 2.1412 , 0.1893
E) 1.9883 , 0.1758
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k this deck
19
The initial investment in a savings account in which interest is compounded continuously is $813. If the time required to double the amount is years, what is the annual rate? Round your answer to two decimal places.
A) 7.49 %
B) 7.70 %
C) 13.34 %
D) 6.29 %
E) 8.89 %
years, what is the annual rate? Round your answer to two decimal places.A) 7.49 %
B) 7.70 %
C) 13.34 %
D) 6.29 %
E) 8.89 %
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20
Find the principal that must be invested at the rate 8%, compounded monthly, so that $1,000,000 will be available for retirement in 50 years. Round your answer to the nearest cent.
A) $250,000.00
B) $18,560.39
C) $717,324.37
D) $333,333.33
E) $21,321.23
A) $250,000.00
B) $18,560.39
C) $717,324.37
D) $333,333.33
E) $21,321.23
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21
The number of bacteria in a culture is increasing according to the law of exponential growth. After 5 hours there are 175 bacteria in the culture and after 10 hours there are 425 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. (i) Find the initial population.
(ii) Write an exponential growth model for the bacteria population. Let t represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000?
A) (i) 72.0588 ; (ii) ; (iii) 3,819.3668 ; (iv) 32.4162 hr
B) (i) 74.2088 ; (ii) ; (iii) 5,194.0840 ; (iv) 34.6442 hr
C) (i) 72.0588 ; (ii) ; (iii) 2,506.6327 ; (iv) 30.0817 hr
D) (i) 77.8388 ; (ii) ; (iii) 7,945.5374 ; (iv) 36.7554 hr
E) (i) 79.3988 ; (ii) ; (iii) 10,598.0009 ; (iv) 38.5348 hr
(ii) Write an exponential growth model for the bacteria population. Let t represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000?
A) (i) 72.0588 ; (ii)
; (iii) 3,819.3668 ; (iv) 32.4162 hrB) (i) 74.2088 ; (ii)
; (iii) 5,194.0840 ; (iv) 34.6442 hrC) (i) 72.0588 ; (ii)
; (iii) 2,506.6327 ; (iv) 30.0817 hrD) (i) 77.8388 ; (ii)
; (iii) 7,945.5374 ; (iv) 36.7554 hrE) (i) 79.3988 ; (ii)
; (iii) 10,598.0009 ; (iv) 38.5348 hr Unlock Deck
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22
Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is 0.024. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places.
A)
B)
C)
D)
E)
for the population by letting correspond to 2000. Round your answer to four decimal places.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
23
A container of hot liquid is placed in a freezer that is kept at a constant temperature of . The initial temperature of the liquid is . After 3 minutes, the liquid's temperature is . How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places.
A) 1.89 minutes
B) 2.84 minutes
C) 3.16 minutes
D) 1.26 minutes
E) 3.47 minutes
. The initial temperature of the liquid is . After 3 minutes, the liquid's temperature is . How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places.A) 1.89 minutes
B) 2.84 minutes
C) 3.16 minutes
D) 1.26 minutes
E) 3.47 minutes
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
24
Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected continuous annual rate of change of the population is 0.017. The exponential growth model for the population by letting corresponds to 2000 is . Use the model to predict the population of the country in 2013. Round your answer to two decimal places.
A) 83.08 million
B) 87.42 million
C) 90.45 million
D) 88.92 million
E) 81.68 million
corresponds to 2000 is . Use the model to predict the population of the country in 2013. Round your answer to two decimal places.A) 83.08 million
B) 87.42 million
C) 90.45 million
D) 88.92 million
E) 81.68 million
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25
Find the time (in years) necessary for 1,000 to double if it is invested at a rate 6% compounded continuously. Round your answer to two decimal places.
A) 1.16 years
B) 11.55 years
C) 1.39 years
D) 11.90 years
E) 11.58 years
A) 1.16 years
B) 11.55 years
C) 1.39 years
D) 11.90 years
E) 11.58 years
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