Question 1

Which transformation is applied to the function $$f(x) = 3^x to $$obtain the graph of $$g(x) = -2 \cdot 3$$^{-x}$$ + 4$$?

Accepted Answer

Reflection over the y-axis, vertical stretch by 2, reflection over the x-axis, and vertical shift up 4

Question 2

Given the logarithmic scale (base 10) with values $$0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100$$, what is the position of $$x = 5 on $$this scale?

Accepted Answer

$$\log_{10}(5) \approx 0.70$$

Question 3

A population of dolphins grows according to the equation $$N = 45.12(1.14)^t. $$What is the population after 5 years? (Round to the nearest whole number.)

Accepted Answer

$$N = 87$$

Question 4

Which of the following equations represents a linearized form of the exponential growth equation $$y = ab^x$$ using common logarithms?

Accepted Answer

$$\log(y) = \log(a) + x \log(b)$$

Question 5

If $$y = 24x^3$, what is the linearized form when using logarithms?

Accepted Answer

$$\log(y) = \log(24) + 3\log(x)$$

Question 6

Given the table of values below, which best describes the relationship between $$y$$ and $$x$$?

$$x$$: 0, 1, 2, 3, 4
$$y$$: 8.5, 14.1, 23.4, 38.7, 64.1$

Accepted Answer

$$y = 8.5 \cdot (1.66)^x$$

Question 7

Which of the following best describes the effect of multiplying the input of an exponential function by $$-1 (i.e$$., $$f(-x)$$)?

Accepted Answer

It reflects the graph over the y-axis.

Question 8

Suppose a scientist models bacteria growth with $$N = 100(1.2)^t. $$How long will it take for the population to triple?

Accepted Answer

$$t = \dfrac{\log(3)}{\log(1.2)} \approx 6.3$$

Question 9

If $$y = ab^x$$ and you plot $$\log(y)$$ versus $$x$$, what is the slope of the resulting line?

Accepted Answer

$$\log(b)$$

Question 10

Given $$y = 3e$$^{2x}$$, what is the value of x$ when y = 24$?

Accepted Answer

$$x = \dfrac{1}{2} \ln(8)$$

Question 11

Which of the following is the correct linearized form for a power function $$y = kx^n$$?

Accepted Answer

$$\log(y) = \log(k) + n\log(x)$$

Question 12

A radioactive substance decays according to $$N = N_0$ e$$^{-0.03t}$$. What is the half-life of the substance?

Accepted Answer

$$t_{1/2} = \dfrac{\ln(2)}{0.03}$$

Question 13

If $$y = 7(1.17)^x$$, what is the value of $$x$$ when $$y = 19.7$$?

Accepted Answer

$$x = \dfrac{\log(19.7/7)}{\log(1.17)}$$

Question 14

Which of the following best describes the relationship between $$y$$ and $$x if$$ $$\log(y) is a $$linear function of $$x$$?

Accepted Answer

$$y is an $$exponential function of $$x$$

Logarithmic and Exponential Functions Study Guide (Calculus Context)

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