Question 1

A pie is removed from a $375^{\circ} \mathrm{C}$ oven and cools to $215^{\circ} \mathrm{F}$ after 15 minutes in a room at $72^{\circ} \mathrm{F}$ How long (from the time it is removed from the oven) will it take the pie to cool to $120^{\circ} \mathrm{F} \text { ? }$

Accepted Answer

The answer of A pie is removed from a \(375^{\circ}...

Question 2

Solve for $x: 2^{3 x-1}=16$

Accepted Answer

The answer of Solve for $x: 2^{3 x-1}=16$...

Question 3

A certain company estimates that the computer they plan to buy in 18 months will cost $ \$ 4,200 $. How much money should be deposited now into an account paying $ 5.75 \% $ interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?

Accepted Answer

The answer of A certain company estimates that the computer...

Question 4

Describe the transformations that can be used to transform the graph of
$ y=\log _{3} x $ to $ y=\log _{3}(x+2)+1 $.
Plot the graph of $ y=\log _{3}(x+2)+1 $

Accepted Answer

The answer of Describe the transformations that can be used...

Question 5

Solve the equation 8 - 3 ln x = 12. Give an exact answer as well as its decimal approximation (to the nearest hundredth).

Accepted Answer

The answer of Solve the equation 8 - 3 ln...

Question 6

Graph the function $y=0.25^{x}$

Accepted Answer

The answer of Graph the function $y=0.25^{x}$
...

Question 7

Juan contributes $ \$ 65 $ monthly into an IRA annuity for 20 years. If the account earns 5.6\% annual interest compounded monthly, what is the value of Juan's account after 20 years?

Accepted Answer

The answer of Juan contributes $ \$ 65 $ monthly...

Question 8

Solve the logarithmic equation  log (x+2)+log x=3 log 2  algebraically. Identify any extraneous solutions.

Accepted Answer

The answer of Solve the logarithmic equation  log (x+2)+log...

Question 9

$\text { Write the inverse of the function } f(x)=e^{x+2} \text {. }$

Accepted Answer

The answer of \(\text { Write the inverse of the...

Question 10

Which equation is equivalent to $y=7 x^{5} ?$

Accepted Answer

A)   ln y=ln 7+5 ln x 
B)   y=ln 7+5 ln x 
C)   y=7+5 ln x 
D)   ln y=7+5 ln x 
E)   ln y=ln 7-5 ln x

Question 11

A $ \$ 125,000 $ mortgage requires monthly payments for 30 years at $ 7.5 \% $ APR. How much is each payment?

Accepted Answer

The answer of A $ \$ 125,000 $ mortgage requires...

Question 12

A bank advertises that currently a CD pays  6 %  APR compounded daily (use 365 days a year). What is the effective yield on this CD, to the nearest hundredth?

Accepted Answer

The answer of A bank advertises that currently a CD...

Question 13

Determine the domain of the function $f(x)=\ln \left(4 x-x^{2}\right)$

Accepted Answer

A)  $(-\infty, 0) \cup(4, \infty)$ 
B)   (0,4) 
C)   (-4,0) 
D)  $(-\infty, 1.39)$ 
E)  $(-\infty, 0) \cup(0,4) \cup(4, \infty)$

Question 14

For the function $f(x)=\frac{6}{1+2 e^{-3 x}}$
(a) Find the horizontal asymptotes.
(b) Find the domain and range
(c) Describe the end behavior.

Accepted Answer

The answer of For the function $f(x)=\frac{6}{1+2 e^{-3 x}}$
(a) Find...

Question 15

A certain company estimates that the computer they plan
to buy in 30 months will cost $5,250. How much money
should be deposited now into an account paying 6.25%
interest, compounded monthly so there will be enough
money to pay cash for the computer in 30 months?

Accepted Answer

The answer of A certain company estimates that the computer...

Question 16

For the function $f(x)=\frac{5}{1+4 e^{-2 x}}$:
(a) Find the horizontal asymptotes.
(b) Find the domain and range.
(c) Describe the end behavior.

Accepted Answer

The answer of For the function $f(x)=\frac{5}{1+4 e^{-2 x}}$:
(a) Find...

Question 17

Find the interval(s) where the function $f(x)=3^{-x}$ is decreasing.

Accepted Answer

A)  $(0, \infty)$ 
B)  $(-\infty, 0)$ 
C)  $(-\infty, 0) \cup(0, \infty)$ 
D)  $(-\infty, 3) \cup(3, \infty)$ 
E)  $(-\infty, \infty)$

Question 18

(a) Solve for $x: \log _{3} 81=x$
(b) Solve for $x: \log _{x} 8=\frac{3}{2}$

Accepted Answer

The answer of (a) Solve for $x: \log _{3} 81=x$
(b)...

Question 19

Solve the logarithmic equation $\log _{x} 5=3$
for  x . Leave the answer in radical form.

Accepted Answer

The answer of Solve the logarithmic equation $\log _{x} 5=3$
for...

Question 20

When Jose was born, his grandmother deposited $8,000 into an account paying 6% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

Accepted Answer

The answer of When Jose was born, his grandmother deposited...

Exam 3: Exponential, Logistic, and Logarithmic Functions

A pie is removed from a $375^{\circ} \mathrm{C}$ oven and cools to $215^{\circ} \mathrm{F}$ after 15 minutes in a room at $72^{\circ} \mathrm{F}$ How long (from the time it is removed from the oven) will it take the pie to cool to $120^{\circ} \mathrm{F} \text { ? }$

Solve for $x: 2^{3 x-1}=16$

A certain company estimates that the computer they plan to buy in 18 months will cost $\$ 4,200$ . How much money should be deposited now into an account paying $5.75 \%$ interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?

Solve the equation 8 - 3 ln x = 12. Give an exact answer as well as its decimal approximation (to the nearest hundredth).

Graph the function $y=0.25^{x}$ $Graph the function y=0.25^{x}$

Juan contributes $\$ 65$ monthly into an IRA annuity for 20 years. If the account earns 5.6\% annual interest compounded monthly, what is the value of Juan's account after 20 years?

Solve the logarithmic equation log (x+2)+log x=3 log 2 algebraically. Identify any extraneous solutions.

$\text { Write the inverse of the function } f(x)=e^{x+2} \text {. }$

Which equation is equivalent to $y=7 x^{5} ?$

A $\$ 125,000$ mortgage requires monthly payments for 30 years at $7.5 \%$ APR. How much is each payment?

A bank advertises that currently a CD pays 6 % APR compounded daily (use 365 days a year). What is the effective yield on this CD, to the nearest hundredth?

Determine the domain of the function $f(x) =\ln \left(4 x-x^{2}\right)$

For the function $f(x)=\frac{6}{1+2 e^{-3 x}}$ (a) Find the horizontal asymptotes. (b) Find the domain and range (c) Describe the end behavior.

A certain company estimates that the computer they plan to buy in 30 months will cost $5,250. How much money should be deposited now into an account paying 6.25% interest, compounded monthly so there will be enough money to pay cash for the computer in 30 months?

For the function $f(x)=\frac{5}{1+4 e^{-2 x}}$ : (a) Find the horizontal asymptotes. (b) Find the domain and range. (c) Describe the end behavior.

Find the interval(s) where the function $f(x) =3^{-x}$ is decreasing.

(a) Solve for $x: \log _{3} 81=x$ (b) Solve for $x: \log _{x} 8=\frac{3}{2}$

Solve the logarithmic equation $\log _{x} 5=3$ for x . Leave the answer in radical form.

When Jose was born, his grandmother deposited $8,000 into an account paying 6% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

Exam 3: Exponential, Logistic, and Logarithmic Functions

Solve for x:23x−1=16x: 2^{3 x-1}=16x:23x−1=16

A certain company estimates that the computer they plan to buy in 18 months will cost $4,200 \$ 4,200 $4,200 . How much money should be deposited now into an account paying 5.75% 5.75 \% 5.75% interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?

Describe the transformations that can be used to transform the graph of y=log⁡3x y=\log _{3} x y=log3​x to y=log⁡3(x+2)+1 y=\log _{3}(x+2)+1 y=log3​(x+2)+1 . Plot the graph of y=log⁡3(x+2)+1 y=\log _{3}(x+2)+1 y=log3​(x+2)+1

Solve the equation 8 - 3 ln x = 12. Give an exact answer as well as its decimal approximation (to the nearest hundredth).

Graph the function y=0.25xy=0.25^{x}y=0.25x

Juan contributes $65 \$ 65 $65 monthly into an IRA annuity for 20 years. If the account earns 5.6\% annual interest compounded monthly, what is the value of Juan's account after 20 years?

Solve the logarithmic equation log (x+2)+log x=3 log 2 algebraically. Identify any extraneous solutions.

Write the inverse of the function f(x)=ex+2. \text { Write the inverse of the function } f(x)=e^{x+2} \text {. } Write the inverse of the function f(x)=ex+2.

Which equation is equivalent to y=7x5?y=7 x^{5} ?y=7x5?

A $125,000 \$ 125,000 $125,000 mortgage requires monthly payments for 30 years at 7.5% 7.5 \% 7.5% APR. How much is each payment?

A bank advertises that currently a CD pays 6 % APR compounded daily (use 365 days a year). What is the effective yield on this CD, to the nearest hundredth?

Determine the domain of the function f(x) =ln⁡(4x−x2) f(x) =\ln \left(4 x-x^{2}\right) f(x) =ln(4x−x2)

For the function f(x)=61+2e−3xf(x)=\frac{6}{1+2 e^{-3 x}}f(x)=1+2e−3x6​ (a) Find the horizontal asymptotes. (b) Find the domain and range (c) Describe the end behavior.

A certain company estimates that the computer they plan to buy in 30 months will cost $5,250. How much money should be deposited now into an account paying 6.25% interest, compounded monthly so there will be enough money to pay cash for the computer in 30 months?

For the function f(x)=51+4e−2xf(x)=\frac{5}{1+4 e^{-2 x}}f(x)=1+4e−2x5​ : (a) Find the horizontal asymptotes. (b) Find the domain and range. (c) Describe the end behavior.

Find the interval(s) where the function f(x) =3−xf(x) =3^{-x}f(x) =3−x is decreasing.

(a) Solve for x:log⁡381=xx: \log _{3} 81=xx:log3​81=x (b) Solve for x:log⁡x8=32x: \log _{x} 8=\frac{3}{2}x:logx​8=23​

Solve the logarithmic equation log⁡x5=3\log _{x} 5=3logx​5=3 for x . Leave the answer in radical form.

When Jose was born, his grandmother deposited $8,000 into an account paying 6% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

Solve for $x: 2^{3 x-1}=16$

A certain company estimates that the computer they plan to buy in 18 months will cost $\$ 4,200$ . How much money should be deposited now into an account paying $5.75 \%$ interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?

Graph the function $y=0.25^{x}$ $Graph the function y=0.25^{x}$

Juan contributes $\$ 65$ monthly into an IRA annuity for 20 years. If the account earns 5.6\% annual interest compounded monthly, what is the value of Juan's account after 20 years?

$\text { Write the inverse of the function } f(x)=e^{x+2} \text {. }$

Which equation is equivalent to $y=7 x^{5} ?$

A $\$ 125,000$ mortgage requires monthly payments for 30 years at $7.5 \%$ APR. How much is each payment?

Determine the domain of the function $f(x) =\ln \left(4 x-x^{2}\right)$

For the function $f(x)=\frac{6}{1+2 e^{-3 x}}$ (a) Find the horizontal asymptotes. (b) Find the domain and range (c) Describe the end behavior.

For the function $f(x)=\frac{5}{1+4 e^{-2 x}}$ : (a) Find the horizontal asymptotes. (b) Find the domain and range. (c) Describe the end behavior.

Find the interval(s) where the function $f(x) =3^{-x}$ is decreasing.

(a) Solve for $x: \log _{3} 81=x$ (b) Solve for $x: \log _{x} 8=\frac{3}{2}$

Solve the logarithmic equation $\log _{x} 5=3$ for x . Leave the answer in radical form.