Question 1

Given the function $$y = e$$^{1-x}$$ - 2$$, which of the following statements is TRUE about its horizontal asymptote?

Accepted Answer

The horizontal asymptote is $$y = -2.$$

Question 2

A $$9500 investment earns 5.2% annual interest, compounded semi-annually. What is the value of the investment after 12 years? (Round to the nearest dollar.)

Use A(t) = P$$ \left(1 + \frac{r}{n}\$$right)^{nt}$.

Accepted Answer

$$17,026$$

Question 3

Solve for $$x$$: $$e^{2-3x} = 11$.

Accepted Answer

$$x = \frac{2 - \ln 11}{3}$$

Question 4

A bacteria culture starts with 3200 bacteria and grows to 5000 after 4 hours, following $$P(t) = P_0$ e$$^{kt}$$. What is the value of k$ (rounded to three decimal places)?

Accepted Answer

$$k = 0.117$$

Question 5

A chemical sample decays from 240 grams to 150 grams in 6 days, following $$A(t) = A_0$ e$$^{kt}$$. What is the amount remaining after 10 days? (Round to the nearest gram.)

Accepted Answer

$$94$$ grams

Question 6

If an earthquake has magnitude $$M = 6.3$$, what is the ratio $$\frac{I}{S} as a $$power of 10? (Recall $$M = \log \left(\frac{I}{S}\right).)$$

Accepted Answer

$$10^{6.3}$$

Question 7

Let $$t = \frac{5\pi}{6}. $$What is the reference number for $$t$$?

Accepted Answer

$$\frac{\pi}{6}$$

Question 8

The point $$\left(-\frac{\sqrt{5}}{3}, -\frac{2}{3}ight)$$ lies on the unit circle. What is $$	an t$$?

Accepted Answer

$$\frac{2}{\sqrt{5}}$$

Question 9

Consider the function $$y = -3 \cos(2x - \pi) + 1. $$What is the amplitude of the function?

Accepted Answer

$$3$$

Question 10

Given $$\log(x + 2) + \log(x - 1) = 1$$, what is the solution for $$x$$?

Accepted Answer

$$x = 3$$

Question 11

If $$y = \log_2$(x + 3) - 1$$, what is the domain of the function?

Accepted Answer

$$x \u003e -3$$

Question 12

For the function $$y = -\ln(x - 1) + 2$$, what is the $$y-$$intercept?

Accepted Answer

There is no $$y-$$intercept.

Question 13

Solve for $$x$$: $$4^x = 8$$^{x-1}$$.

Accepted Answer

$$x = 3$$

Question 14

A bacteria culture doubles in size after how many hours, if it starts at 3200 and grows to 5000 in 4 hours? (Round to one decimal place.)

Accepted Answer

$$5.9$$ hours

Question 15

If $$\sin t = -\frac{2}{3}$$ and $$\cos t = -\frac{\sqrt{5}}{3}$$, what is $$\csc t$$?

Accepted Answer

$$-\frac{3}{2}$$

Question 16

Given $$y = -3 \cos(2x - \pi) + 1$$, what is the period of the function?

Accepted Answer

$$\pi$$

Question 17

If one earthquake has magnitude $$6.3$$ and another has magnitude $$4.8$$, how many times as intense is the larger earthquake?

Accepted Answer

$$10^{1.5}$$

Question 18

Solve for $$x$$: $$\ln(x + 5) - 2 = 1.$$

Accepted Answer

$$x = e$$^{3}$$ - 5$$

Question 19

Given $$y = -3 \cos(2x - \pi) + 1$$, what is the equation of the midline?

Accepted Answer

$$y = 1$$

Question 20

Given $$y = \log_2$(x + 3) - 1$$, what is the range of the function?

Accepted Answer

$$(-\infty, \infty)$$

Precalculus Practice Test 2 – Step-by-Step Guidance

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