Question 1

The logistic function   models the growth of a population. Identify the maximum carrying capacity.

Accepted Answer

A)  10 
B)  3.5 
C)  3 
D)  2 
E)  4 
A)  10 
B)  3.5 
C)  3 
D)  2 
E)  4

Question 2

Find the principal that must be invested at the rate 6%, compounded monthly, so that $3,000,000 will be available for retirement in 55 years. Round your answer to the nearest cent. ​

Accepted Answer

A)  $909,090.91 
B)  $111,563.08 
C)  $2,280,278.32 
D)  $825,000.00 
E)  $121,702.27 
A)  $909,090.91 
B)  $111,563.08 
C)  $2,280,278.32 
D)  $825,000.00 
E)  $121,702.27

Question 3

The isotope   has a half-life of 1,599 years. After 20,000 years, a sample of the isotope is reduced 0.7 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places. ​

Accepted Answer

A)  4076.8643 g, 1713.1817 g 
B)  5299.9236 g, 2227.1362 g 
C)  2446.1186 g, 1027.9090 g 
D)  3261.4914 g, 1370.5454 g 
E)  2038.4321 g, 856.5909 g 
A)  4076.8643 g, 1713.1817 g 
B)  5299.9236 g, 2227.1362 g 
C)  2446.1186 g, 1027.9090 g 
D)  3261.4914 g, 1370.5454 g 
E)  2038.4321 g, 856.5909 g

Question 4

The half-life of the radium isotope Ra-226 is approximately 1,599 years. What percent of a given amount remains after 200 years? Round your answer to two decimal places. ​

Accepted Answer

A)  91.70 % 
B)  5.92 % 
C)  93.70 % 
D)  6.25 % 
E)  0.92 % 
A)  91.70 % 
B)  5.92 % 
C)  93.70 % 
D)  6.25 % 
E)  0.92 %

Question 5

The isotope   has a half-life of   years. Given an initial amount of 16 grams of the isotope, how many grams will remain after 1,000 years? After 10,000 years? Round your answers to four decimal places. ​

Accepted Answer

A)  10.8825 g, 8.4006 g 
B)  9.3278 g, 7.2005 g 
C)  15.5464 g, 12.0008 g 
D)  6.2185 g, 4.8003 g 
E)  18.6556 g, 14.4010 g 
A)  10.8825 g, 8.4006 g 
B)  9.3278 g, 7.2005 g 
C)  15.5464 g, 12.0008 g 
D)  6.2185 g, 4.8003 g 
E)  18.6556 g, 14.4010 g

Question 6

Find the particular solution of the differential equation   that satisfies the initial condition   when   , where   is the general solution. ​

Accepted Answer