Exam 3: Exponential, Logistic, and Logarithmic Functions

$\text { Describe the end behavior of the function }$ $g(x)=\left(\frac{2}{3}\right)^{x}$ g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty

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Question 1

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$\begin{array}{l}g(x) \rightarrow \underline{ \quad \quad \infty \quad\quad } \text { as } x \rightarrow-\infty ; g(x) \rightarrow \underline{\quad\quad0\quad\quad}\\\text { as } x \rightarrow \infty\end{array}$

Graph the function $y=3^{-x}$ $Graph the function y=3^{-x}$

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Solve $e^{x^{2}}+5 x-1=0$ graphically.

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Question 3

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x=-1.45,0

Solve the equation log (x-4)+log (x+5)=1 algebraically. List any extraneous solutions and explain If there are no extraneous solutions, explain why not.

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Question 4

Show that $f(x)=\frac{1}{4} \ln x \text { and } g(x)=e^{4 x}$ are inverse functions.

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Question 5

To finance their new home, the Tiballis have agreed to an $80,000 mortgage loan at 8.75% APR. What will their monthly payments be if the loan has a term of 20 years?

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Question 6

A casserole is removed from an oven at $375^{\circ} \mathrm{F}$ and cools to $190^{\circ} \mathrm{F}$ after 25 minutes in a room at $68^{\circ} \mathrm{F}$ How long (from the time it is removed from the oven) will it take the casserole to cool to $105^{\circ} \mathrm{F} \text { ? }$

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Question 7

When Kara was born, her grandmother deposited $10,500 into an account paying 6.4% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

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Question 8

How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a $1000?

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Question 9

Juan deposits $200 each month into a retirement account that pays 9.00% APR (0.75% per month). What is the value of this annuity after 30 years?

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Question 10

To finance their new home, the Colemans have agreed to a $90,000 mortgage loan at 9.25% APR. What will their monthly payments be if the loan has a term of 15 years?

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Question 11

(a) Solve for $x: \log _{4} 64=x$ (b) Solve for $x: \log _{x} 3=\frac{1}{2}$

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Question 12

What is the natural logarithmic regression equation for the following data? Estimate the y-value for x = 18. Express answers to the nearest hundredth. x 3 5 9 12 y 4 7 10 11

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Question 13

Write the exponential equation $3^{x}=9$ in logarithmic form.

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Question 14

Let $S=a(1.06)^{t}$ Solve for t .

(Multiple Choice)

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Question 15

The population of Powerville is 425,000 , and it is increasing at a rate of 4.2% each year. Predict the number of years until the population will be 750,000 . Round to two decimal places.

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Question 16

Graph the logistic function $f(x)=\frac{15}{1+e^{-2 x}}$ Show the viewing window dimensions.

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Question 17

Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$

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Question 18

Solve the log (x-5)+log (x-2)=1 algebraically. List any extraneous solutions and explain. If there are no extraneous solutions, explain why not.

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Question 19

What is the value of $\log _{5} 14$ , accurate to two decimal places?

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Question 20

$\text { Describe the end behavior of the function }$ $g(x)=\left(\frac{2}{3}\right)^{x}$ g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty

Graph the function $y=3^{-x}$ $Graph the function y=3^{-x}$

Solve $e^{x^{2}}+5 x-1=0$ graphically.

Solve the equation log (x-4)+log (x+5)=1 algebraically. List any extraneous solutions and explain If there are no extraneous solutions, explain why not.

Show that $f(x)=\frac{1}{4} \ln x \text { and } g(x)=e^{4 x}$ are inverse functions.

To finance their new home, the Tiballis have agreed to an $80,000 mortgage loan at 8.75% APR. What will their monthly payments be if the loan has a term of 20 years?

A casserole is removed from an oven at $375^{\circ} \mathrm{F}$ and cools to $190^{\circ} \mathrm{F}$ after 25 minutes in a room at $68^{\circ} \mathrm{F}$ How long (from the time it is removed from the oven) will it take the casserole to cool to $105^{\circ} \mathrm{F} \text { ? }$

When Kara was born, her grandmother deposited $10,500 into an account paying 6.4% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a $1000?

Juan deposits $200 each month into a retirement account that pays 9.00% APR (0.75% per month). What is the value of this annuity after 30 years?

To finance their new home, the Colemans have agreed to a $90,000 mortgage loan at 9.25% APR. What will their monthly payments be if the loan has a term of 15 years?

(a) Solve for $x: \log _{4} 64=x$ (b) Solve for $x: \log _{x} 3=\frac{1}{2}$

What is the natural logarithmic regression equation for the following data? Estimate the y-value for x = 18. Express answers to the nearest hundredth. x 3 5 9 12 y 4 7 10 11

Write the exponential equation $3^{x}=9$ in logarithmic form.

Let $S=a(1.06)^{t}$ Solve for t .

The population of Powerville is 425,000 , and it is increasing at a rate of 4.2% each year. Predict the number of years until the population will be 750,000 . Round to two decimal places.

Graph the logistic function $f(x)=\frac{15}{1+e^{-2 x}}$ Show the viewing window dimensions.

Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$

Solve the log (x-5)+log (x-2)=1 algebraically. List any extraneous solutions and explain. If there are no extraneous solutions, explain why not.

What is the value of $\log _{5} 14$ , accurate to two decimal places?

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 3: Exponential, Logistic, and Logarithmic Functions

Describe the end behavior of the function \text { Describe the end behavior of the function } Describe the end behavior of the function g(x)=(23)xg(x)=\left(\frac{2}{3}\right)^{x}g(x)=(32​)x g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty

Graph the function y=3−xy=3^{-x}y=3−x

Solve ex2+5x−1=0e^{x^{2}}+5 x-1=0ex2+5x−1=0 graphically.

Solve the equation log (x-4)+log (x+5)=1 algebraically. List any extraneous solutions and explain If there are no extraneous solutions, explain why not.

Show that f(x)=14ln⁡x and g(x)=e4xf(x)=\frac{1}{4} \ln x \text { and } g(x)=e^{4 x}f(x)=41​lnx and g(x)=e4x are inverse functions.

To finance their new home, the Tiballis have agreed to an $80,000 mortgage loan at 8.75% APR. What will their monthly payments be if the loan has a term of 20 years?

When Kara was born, her grandmother deposited $10,500 into an account paying 6.4% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a $1000?

Juan deposits $200 each month into a retirement account that pays 9.00% APR (0.75% per month). What is the value of this annuity after 30 years?

To finance their new home, the Colemans have agreed to a $90,000 mortgage loan at 9.25% APR. What will their monthly payments be if the loan has a term of 15 years?

(a) Solve for x:log⁡464=xx: \log _{4} 64=xx:log4​64=x (b) Solve for x:log⁡x3=12x: \log _{x} 3=\frac{1}{2}x:logx​3=21​

What is the natural logarithmic regression equation for the following data? Estimate the y-value for x = 18. Express answers to the nearest hundredth. x 3 5 9 12 y 4 7 10 11

Write the exponential equation 3x=93^{x}=93x=9 in logarithmic form.

Let S=a(1.06)tS=a(1.06)^{t}S=a(1.06)t Solve for t .

The population of Powerville is 425,000 , and it is increasing at a rate of 4.2% each year. Predict the number of years until the population will be 750,000 . Round to two decimal places.

Graph the logistic function f(x)=151+e−2xf(x)=\frac{15}{1+e^{-2 x}}f(x)=1+e−2x15​ Show the viewing window dimensions.

Which expression is equivalent to ln x105?\sqrt[5]{\frac{x}{10}} ?510x​​?

Solve the log (x-5)+log (x-2)=1 algebraically. List any extraneous solutions and explain. If there are no extraneous solutions, explain why not.

What is the value of log⁡514 \log _{5} 14 log5​14 , accurate to two decimal places?

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

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$\text { Describe the end behavior of the function }$ $g(x)=\left(\frac{2}{3}\right)^{x}$ g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty

Graph the function $y=3^{-x}$ $Graph the function y=3^{-x}$

Solve $e^{x^{2}}+5 x-1=0$ graphically.

Show that $f(x)=\frac{1}{4} \ln x \text { and } g(x)=e^{4 x}$ are inverse functions.

(a) Solve for $x: \log _{4} 64=x$ (b) Solve for $x: \log _{x} 3=\frac{1}{2}$

Write the exponential equation $3^{x}=9$ in logarithmic form.

Let $S=a(1.06)^{t}$ Solve for t .

Graph the logistic function $f(x)=\frac{15}{1+e^{-2 x}}$ Show the viewing window dimensions.

Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$

What is the value of $\log _{5} 14$ , accurate to two decimal places?