Q: A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

$$P(t) = 500 \times 2$$^{t/3}$$

Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function that can be written as $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$n is a $$positive integer and the coefficients $$a_i$ are real numbers.

Question 2

Given the function $$f(x) = 2x^3$ - 5x^2$ + 4x - 7$$, what is the degree of the polynomial?

Accepted Answer

3

Question 3

Which of the following is the correct domain for the function $$f(x) = \log_2$(x-3)$$?

Accepted Answer

$$x \u003e 3$$

Question 4

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 	imes 2$$^{t/3}$$

Question 5

Which of the following is the inverse function of $$f(x) = e$$^{x}$$?

Accepted Answer

$$f^{-1}(x$$) = \ln(x)$$

Question 6

If $$f(x) = \sin(x)$$ and $$g(x) = \cos(x)$$, what is $$f(x)^2$$ + $$g(x)^2$$ for all $$x$$?

Accepted Answer

$$1$$

Question 7

Which of the following is the correct formula for the period of the function $$f(x) = 	an(x)$$?

Accepted Answer

$$\pi$$

Question 8

A ramp rises 3 meters vertically and runs 4 meters horizontally. What is the angle of elevation of the ramp, in degrees?

Accepted Answer

$$\arctan\left(\frac{3}{4}\right)$$

Question 9

Which of the following is the correct expression for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ ($$|r| \u003c 1) $$over $$n$$ terms?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Question 10

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 11

Which of the following is the correct solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 12

A sound wave has a frequency modeled by $$f(t) = 100 \sin(2\pi t)$$, where $$t is in $$seconds. What is the period of the wave?

Accepted Answer

$$1$$ second

Question 13

Which of the following is the correct formula for the compound interest after $$t$$ years, with principal $$P$$, annual rate $$r$$, and $$n$$ compounding periods per year?

Accepted Answer

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

Question 14

Which of the following is the correct expression for the cosine of a sum, $$\cos(A + B)$$?

Accepted Answer

$$\cos(A + B) = \cos A \cos B - \sin A \sin B$$

Question 15

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 16

Which of the following is the correct definition of an even function?

Accepted Answer

A function $$f is $$even if $$f(-x) = f(x)$$ for all $$x in $$the domain.

Question 17

Which of the following is the correct solution to $$\sin(x) = \frac{1}{2}$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 18

Which of the following is the correct formula for the natural logarithm of a product, $$\ln(ab)$$?

Accepted Answer

$$\ln(ab) = \ln a + \ln b$$

Question 19

A Ferris wheel has a radius of 20 meters. What is the height above the ground of a seat at an angle $$	heta$$ from the horizontal, if the center is 25 meters above the ground?

Accepted Answer

$$h = 25 + 20\sin(	heta)$$

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