Quiz about Chapter 6 Review

Question 1

Tell whether the function represents exponential growth or decay. $$y=\left(1.6\right)^x$$

Accepted Answer

growth

Answer

decay

Answer

impossible to tell

Answer

D.

Question 2

The value of a rare coin $$y$$ (in dollars) can be approximated by the model: $$y=0.25\left(1.06\right)^t$$ , where $$t$$ is the number of years since the coin was minted. Tell whether the model represents exponential growth or decay:

Accepted Answer

growth

Answer

decay

Answer

impossible to tell

Answer

Why can't I just play rocket league all day?

Question 3

The value of a rare coin $$y$$ (in dollars) can be approximated by the model: $$y=0.25\left(1.06\right)^t$$ , where $$t$$ is the number of years since the coin was minted. Identify the annual percent increase or decrease in the value of the coin.

Accepted Answer

6% increase

Answer

6% decrease

Answer

94% increase

Answer

94% decrease

Question 4

The value of a rare coin $$y$$ (in dollars) can be approximated by the model: $$y=0.25\left(1.06\right)^t$$ , where $$t$$ is the number of years since the coin was minted. What was the original value of the coin?

Accepted Answer

25 cents

Answer

35 cents

Answer

One dollar and six cents

Answer

75 cents

Question 5

$$e^{-3}\cdot e^8=$$

Accepted Answer

$$e^5$$

Answer

$$e^{-\frac{3}{8}}$$

Answer

$$24e$$

Answer

$$e^{-24}$$

Question 6

Tell whether function represents exponential growth or decay: $$y=e^{-x}$$ . Where does the function cross the $$y$$ axis?

Accepted Answer

decay, crosses at (0,1)

Answer

growth, crosses at (0,1)

Answer

growth, crosses at (1,0)

Answer

decay, crosses at (1,0)

Question 7

Simplify: $$\left(2e^{3x}\right)^3$$

Accepted Answer

$$8e^{9x}$$

Answer

$$2e^{9x}$$

Answer

$$8e^{6x}$$

Answer

$$2e^{6x}$$

Question 8

#4 on p. 353 (hint - plot f(x) in your calculator and compare)

Accepted Answer

Reflect over x-axis and translate 4 right

$$g\left(x\right)=-\log\left(x-4\right)$$

Answer

Reflect over x-axis and translate 2 right

$$g\left(x\right)=-\log\left(x-2\right)$$

Answer

Reflect over x-axis and translate 2 left

$$g\left(x\right)=-\log\left(x+2\right)$$

Answer

Reflect over x-axis and translate 4 left

$$g\left(x\right)=-\log\left(x+4\right)$$

Question 9

#5 on p. 353 (hint - plot f(x) in your calculator and compare)

Accepted Answer

Reflect across y-axis and translate 2 units up

$$g\left(x\right)=e^{-x}+2$$

Answer

Reflect across y-axis and translate 3 units up

$$g\left(x\right)=e^{-x}+3$$

Answer

Reflect across x-axis and translate 3 units up

$$g\left(x\right)=-e^x+3$$

Answer

Reflect across x-axis and translate 2 units up

$$g\left(x\right)=-e^x+2$$

Question 10

#6 on p. 353 (hint - plot f(x) in your calculator and compare)

Accepted Answer

Vertical stretch by a factor of 2

$$y=2\left(\frac{1}{4}\right)^x$$

Answer

Vertical stretch by a factor of 3

$$y=3\left(\frac{1}{4}\right)^x$$

Answer

Horizontal stretch by a factor of 2

$$y=\left(\frac{1}{4}\right)^{\frac{x}{2}}$$

Answer

Horizontal stretch by a factor of 2

$$y=\left(\frac{1}{4}\right)^{\frac{x}{3}}$$

Question 11

Rewrite the equation in exponential form: $$\log_{10}1000=3$$

Accepted Answer

$$10^3=1000$$

Answer

$$10^{1000}=$$ "error"

Answer

$$3^{10}=59049$$

Answer

$$\frac{1000}{3}=333.333$$

Question 12

Rewrite the equation in logarithmic form: $$20^{-1}=\frac{1}{20}$$

Accepted Answer

$$\log_{20}\left(\frac{1}{20}\right)=-1$$

Answer

$$\log_{-1}\left(20\right)=\frac{1}{20}$$

Answer

$$\log_{20}\left(-1\right)=\frac{1}{20}$$

Answer

$$\log_{20}\left(20^{-1}\right)=20$$

Question 13

Expand $$\ln\left(\frac{12x^5}{y}\right)$$

Accepted Answer

$$\ln\left(12\right)+5\ln\left(x\right)-\ln\left(y\right)$$

Answer

$$\ln\left(12\right)-\ln\left(x^5\right)-\ln\left(y\right)$$

Answer

$$\ln\left(12x\right)-5y$$

Answer

$$\frac{\ln\left(12x^5\right)}{\ln\left(y\right)}$$

Question 14

Condense: $$\log_212-2\log_2x$$

Accepted Answer

$$\log_2\left(\frac{12}{x^2}\right)$$

Answer

$$\log_2\left(\frac{x}{6}\right)$$

Answer

$$e^{\left(\frac{12}{x^2}\right)}$$

Answer

$$\log_x\left(\frac{12}{2x}\right)$$

Question 15

Solve the equation for $$x$$ : $$\ln\left(x\right)=9$$

Accepted Answer

$$x=e^9$$

Answer

$$x=2^9$$

Answer

$$x=10^9$$

Answer

$$x=e^{\ln\left(x-9\right)}$$

Chapter 6 Review

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