Question 1

How many relative extrema does $x ^ { 4 } e ^ { x }$ have on the domain (-10, 10)?

Accepted Answer

The answer of How many relative extrema does \(x ^...

Question 2

How many years old is a fossil in which the ratio of ${ } ^ { 14 } \mathrm { C }$ to ${ } ^ { 12 } \mathrm { C }$ is $\frac { 1 } { 7 }$ the ratio found in the atmosphere? The half-life of ${ } ^ { 14 } \mathrm { C }$ is 5,730 years. Round to the nearest whole year.

Accepted Answer

The answer of How many years old is a fossil...

Question 3

Differentiate the given function. $$f ( x ) = e ^ { - 5 x }$$

Accepted Answer

A)  $x = - 5 e ^ { - 5 x }$ 
B)  $x = - 5 x e ^ { - 5 x }$ 
C)  $x = e ^ { - 5 x }$ 
D)  $x = - 5 e ^ { - 5 x - 1 }$ 
A)  $x = - 5 e ^ { - 5 x }$ 
B)  $x = - 5 x e ^ { - 5 x }$ 
C)  $x = e ^ { - 5 x }$ 
D)  $x = - 5 e ^ { - 5 x - 1 }$

Question 4

The function $f ( x ) = e ^ { x }$ is increasing everywhere.

Accepted Answer

A) True 
 B)False

Question 5

Let $f ( t ) = \frac { 19 } { 3 + 4 e ^ { - t / 10 } }$ Which value of t corresponds to a possible inflection pointfor f(t) ?

Accepted Answer

A)  There is no inflection point. 
B)  $\frac { 3 } { 4 } \ln ( 110 )$ 
C)  $\ln \left( \frac { 3 } { 4 } \right)$ 
D)  $110 \ln \left( \frac { 4 } { 3 } \right)$ 
A)  There is no inflection point. 
B)  $\frac { 3 } { 4 } \ln ( 110 )$ 
C)  $\ln \left( \frac { 3 } { 4 } \right)$ 
D)  $110 \ln \left( \frac { 4 } { 3 } \right)$

Question 6

Solve the given equation for x. $- 6 = - 7 + 5 e ^ { - 7 x }$

Accepted Answer

A)  $- \frac { e ^ { 5 } } { 7 }$ 
B)  $\frac { \ln 5 } { 7 }$ 
C)  $- 7 e ^ { 5 }$ 
D)  $- \frac { \ln 5 } { 7 }$ 
A)  $- \frac { e ^ { 5 } } { 7 }$ 
B)  $\frac { \ln 5 } { 7 }$ 
C)  $- 7 e ^ { 5 }$ 
D)  $- \frac { \ln 5 } { 7 }$

Question 7

Find the present value, in dollars, of $10,000 payable 8 years from now if the annual interest rate is 7% compounded continuously.

Accepted Answer

The answer of Find the present value, in dollars, of...

Question 8

Evaluate the expression $e ^ { 2 \ln 8 - 3 \ln 6 }$ without using tables or calculators.

Accepted Answer

The answer of Evaluate the expression \(e ^ { 2...

Question 9

Solve for x: $$4 \ln x - \frac { 1 } { 5 } \ln x ^ { 4 } = 16$$

Accepted Answer

A)  x = e 
B)  $x = e ^ { 16 }$ 
C)  $x = e ^ { 4 }$ 
D)  $x = e ^ { 5 }$ 
A)  x = e 
B)  $x = e ^ { 16 }$ 
C)  $x = e ^ { 4 }$ 
D)  $x = e ^ { 5 }$

Question 10

The equation of the tangent line to $f ( x ) = 3 \ln x ^ { 2 }$ at x = e is

Accepted Answer

A)  $y = \frac { 6 x } { e } - 6$ 
B)  $y = \frac { 6 x } { e }$ 
C)  $y = \frac { 6 x } { e ^ { 2 } }$ 
D)  y = 6x 
A)  $y = \frac { 6 x } { e } - 6$ 
B)  $y = \frac { 6 x } { e }$ 
C)  $y = \frac { 6 x } { e ^ { 2 } }$ 
D)  y = 6x

Question 11

The equation of the tangent line to $f ( x ) = 8 x e ^ { x }$ at x = 6 is

Accepted Answer

The answer of The equation of the tangent line to...

Question 12

Solve for x if $\log _ { 6 } ( 2 x ) = 5$ .

Accepted Answer

The answer of Solve for x if \(\log _ {...

Question 13

Solve for x: $\log _ { 6 } ( x - 1 ) = 5$ .

Accepted Answer

A)  7,777 
B)  7,776 
C)  7,775 
D)  15,626 
A)  7,777 
B)  7,776 
C)  7,775 
D)  15,626

Question 14

Sketch the graph of $f ( x ) = 3 - e ^ { x }$ .

Accepted Answer

The answer of Sketch the graph of \(f ( x...

Question 15

Money triples in 15.50 years if it doubles in 10 years. Assume continuous compounding and rounding to two decimal places.

Accepted Answer

A) True 
 B)False

Question 16

An economist estimates that the gross national product (GNP) of a certain country is $G = G _ { 0 } e ^ { k t }$ , where $G _ { 0 }$ and k are positive constants. If the GNP is 110 billion in 1992 and 190 billion in 1994, when will it be 300 billion? Round your answer to whole years.

Accepted Answer

A)  Approximately 5 years from 1992 
B)  Approximately 27 years from 1992 
C)  Approximately 4 years from 1992 
D)  Approximately -1 years from 1992 
A)  Approximately 5 years from 1992 
B)  Approximately 27 years from 1992 
C)  Approximately 4 years from 1992 
D)  Approximately -1 years from 1992

Question 17

If $1,000 is invested at 4 percent compounded continuously, what is the balance after 12 years?

Accepted Answer

A)  $618.78 
B)  $1,040.00 
C)  $1,616.07 
D)  $1,601.03 
A)  $618.78 
B)  $1,040.00 
C)  $1,616.07 
D)  $1,601.03

Question 18

The consumer demand for a certain commodity is $D ( p ) = 5,000 e ^ { - 0.03 p }$ units per month when the market price is p dollars per unit. Determine the market price that will result in the greatest consumer expenditure.

Accepted Answer

A)  $30.31 
B)  $31.31 
C)  $33.33 
D)  $34.33 
A)  $30.31 
B)  $31.31 
C)  $33.33 
D)  $34.33

Question 19

Suppose your family owns a rare book whose value t years from now will be $V ( t ) = 7 e ^ { \sqrt { 0.6 t } }$ dollars. If the prevailing interest rate remains constant at 6% per year compounded continuously, when will it be most advantageous for your family to sell the book and invest the proceeds? Round your answer to two decimal places.

Accepted Answer

A)  34.72 years 
B)  41.67 years 
C)  111.11 years 
D)  180.56 years 
A)  34.72 years 
B)  41.67 years 
C)  111.11 years 
D)  180.56 years

Question 20

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 27 } \right) ^ { x - 1 } = 3 ^ { 3 - 2 x ^ { 2 } }$

Accepted Answer

The answer of Find all real numbers x that satisfy...

How many relative extrema does $x ^ { 4 } e ^ { x }$ have on the domain (-10, 10)?

How many years old is a fossil in which the ratio of ${ } ^ { 14 } \mathrm { C }$ to ${ } ^ { 12 } \mathrm { C }$ is $\frac { 1 } { 7 }$ the ratio found in the atmosphere? The half-life of ${ } ^ { 14 } \mathrm { C }$ is 5,730 years. Round to the nearest whole year.

Differentiate the given function. $f ( x ) = e ^ { - 5 x }$

The function $f ( x ) = e ^ { x }$ is increasing everywhere.

Let $f ( t ) = \frac { 19 } { 3 + 4 e ^ { - t / 10 } }$ Which value of t corresponds to a possible inflection pointfor f(t) ?

Solve the given equation for x. $- 6 = - 7 + 5 e ^ { - 7 x }$

Find the present value, in dollars, of $10,000 payable 8 years from now if the annual interest rate is 7% compounded continuously.

Evaluate the expression $e ^ { 2 \ln 8 - 3 \ln 6 }$ without using tables or calculators.

Solve for x: $4 \ln x - \frac { 1 } { 5 } \ln x ^ { 4 } = 16$

The equation of the tangent line to $f ( x ) = 3 \ln x ^ { 2 }$ at x = e is

The equation of the tangent line to $f ( x ) = 8 x e ^ { x }$ at x = 6 is

Solve for x if $\log _ { 6 } ( 2 x ) = 5$ .

Solve for x: $\log _ { 6 } ( x - 1 ) = 5$ .

Sketch the graph of $f ( x ) = 3 - e ^ { x }$ .

Money triples in 15.50 years if it doubles in 10 years. Assume continuous compounding and rounding to two decimal places.

An economist estimates that the gross national product (GNP) of a certain country is $G = G _ { 0 } e ^ { k t }$ , where $G _ { 0 }$ and k are positive constants. If the GNP is 110 billion in 1992 and 190 billion in 1994, when will it be 300 billion? Round your answer to whole years.

If $1,000 is invested at 4 percent compounded continuously, what is the balance after 12 years?

The consumer demand for a certain commodity is $D ( p ) = 5,000 e ^ { - 0.03 p }$ units per month when the market price is p dollars per unit. Determine the market price that will result in the greatest consumer expenditure.

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 27 } \right) ^ { x - 1 } = 3 ^ { 3 - 2 x ^ { 2 } }$

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

Exam 4: Exponential and Logarithmic Functions

How many relative extrema does x4exx ^ { 4 } e ^ { x }x4ex have on the domain (-10, 10)?

How many years old is a fossil in which the ratio of 14C{ } ^ { 14 } \mathrm { C }14C to 12C{ } ^ { 12 } \mathrm { C }12C is 17\frac { 1 } { 7 }71​ the ratio found in the atmosphere? The half-life of 14C{ } ^ { 14 } \mathrm { C }14C is 5,730 years. Round to the nearest whole year.

Differentiate the given function. f(x)=e−5xf ( x ) = e ^ { - 5 x }f(x)=e−5x

The function f(x)=exf ( x ) = e ^ { x }f(x)=ex is increasing everywhere.

Let f(t)=193+4e−t/10f ( t ) = \frac { 19 } { 3 + 4 e ^ { - t / 10 } }f(t)=3+4e−t/1019​ Which value of t corresponds to a possible inflection pointfor f(t) ?

Solve the given equation for x. −6=−7+5e−7x- 6 = - 7 + 5 e ^ { - 7 x }−6=−7+5e−7x

Find the present value, in dollars, of $10,000 payable 8 years from now if the annual interest rate is 7% compounded continuously.

Evaluate the expression e2ln⁡8−3ln⁡6e ^ { 2 \ln 8 - 3 \ln 6 }e2ln8−3ln6 without using tables or calculators.

Solve for x: 4ln⁡x−15ln⁡x4=164 \ln x - \frac { 1 } { 5 } \ln x ^ { 4 } = 164lnx−51​lnx4=16

The equation of the tangent line to f(x)=3ln⁡x2f ( x ) = 3 \ln x ^ { 2 }f(x)=3lnx2 at x = e is

The equation of the tangent line to f(x)=8xexf ( x ) = 8 x e ^ { x }f(x)=8xex at x = 6 is

Solve for x if log⁡6(2x)=5\log _ { 6 } ( 2 x ) = 5log6​(2x)=5 .

Solve for x: log⁡6(x−1)=5\log _ { 6 } ( x - 1 ) = 5log6​(x−1)=5 .

Sketch the graph of f(x)=3−exf ( x ) = 3 - e ^ { x }f(x)=3−ex .

Money triples in 15.50 years if it doubles in 10 years. Assume continuous compounding and rounding to two decimal places.

If $1,000 is invested at 4 percent compounded continuously, what is the balance after 12 years?

The consumer demand for a certain commodity is D(p)=5,000e−0.03pD ( p ) = 5,000 e ^ { - 0.03 p }D(p)=5,000e−0.03p units per month when the market price is p dollars per unit. Determine the market price that will result in the greatest consumer expenditure.

Find all real numbers x that satisfy the given equation. (127)x−1=33−2x2\left( \frac { 1 } { 27 } \right) ^ { x - 1 } = 3 ^ { 3 - 2 x ^ { 2 } }(271​)x−1=33−2x2

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

How many relative extrema does $x ^ { 4 } e ^ { x }$ have on the domain (-10, 10)?

How many years old is a fossil in which the ratio of ${ } ^ { 14 } \mathrm { C }$ to ${ } ^ { 12 } \mathrm { C }$ is $\frac { 1 } { 7 }$ the ratio found in the atmosphere? The half-life of ${ } ^ { 14 } \mathrm { C }$ is 5,730 years. Round to the nearest whole year.

Differentiate the given function. $f ( x ) = e ^ { - 5 x }$

The function $f ( x ) = e ^ { x }$ is increasing everywhere.

Let $f ( t ) = \frac { 19 } { 3 + 4 e ^ { - t / 10 } }$ Which value of t corresponds to a possible inflection pointfor f(t) ?

Solve the given equation for x. $- 6 = - 7 + 5 e ^ { - 7 x }$

Evaluate the expression $e ^ { 2 \ln 8 - 3 \ln 6 }$ without using tables or calculators.

Solve for x: $4 \ln x - \frac { 1 } { 5 } \ln x ^ { 4 } = 16$

The equation of the tangent line to $f ( x ) = 3 \ln x ^ { 2 }$ at x = e is

The equation of the tangent line to $f ( x ) = 8 x e ^ { x }$ at x = 6 is

Solve for x if $\log _ { 6 } ( 2 x ) = 5$ .

Solve for x: $\log _ { 6 } ( x - 1 ) = 5$ .

Sketch the graph of $f ( x ) = 3 - e ^ { x }$ .

The consumer demand for a certain commodity is $D ( p ) = 5,000 e ^ { - 0.03 p }$ units per month when the market price is p dollars per unit. Determine the market price that will result in the greatest consumer expenditure.

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 27 } \right) ^ { x - 1 } = 3 ^ { 3 - 2 x ^ { 2 } }$