Q: A researcher is studying the cooling of a cup of coffee. The temperature $$T (in $$degrees Celsius) at time $$t (in $$minutes) is modeled by $$T(t) = 20 + 60e$$^{-0.1t}$$. What is the temperature of the coffee after 10 minutes? (Use e$$^{-1}$$ \approx 0.37)$$

$$T(10) = 20 + 60 \times 0.37 = 42.2$$

Q: A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

$$P(t) = 200 \times 2$$^{t/3}$$

Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 1$$?

As $$x \to \pm\infty$$, $$f(x) \to -\infty$$

Question 1

A researcher is studying the cooling of a cup of coffee. The temperature $$T (in $$degrees Celsius) at time $$t (in $$minutes) is modeled by $$T(t) = 20 + 60e$$^{-0.1t}$$. What is the temperature of the coffee after 10 minutes? (Use e$$^{-1}$$ \approx 0.37)$$

Accepted Answer

$$T(10) = 20 + 60 	imes 0.37 = 42.2$$

Question 2

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the equation of the line passing through them?

Accepted Answer

$$y = 2x + 1$$

Question 3

Which of the following best describes the purpose of a best fit line in data analysis?

Accepted Answer

To minimize the sum of the squared vertical distances between the data points and the line

Question 4

Suppose $$f(x) = x^2$ - 4x + 3. $$What is the vertex of this parabola?

Accepted Answer

$$(2, -1)$$

Question 5

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \dfrac{1}{x}$$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 	imes 2$$^{t/3}$$

Question 7

Evaluate $$\log_3$(81).$$

Accepted Answer

$$4$$

Question 8

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

If $$r is $$close to $$0$$, the linear fit is poor.

Question 9

Given $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 10

Which of the following is the equation of a line perpendicular to $$y = -\frac{1}{2}x + 3$$ and passing through $$(0, 1)$$?

Accepted Answer

$$y = 2x + 1$$

Question 11

If $$f(x) = 3x + 2$$, what is $$f(5)$$?

Accepted Answer

$$17$$

Question 12

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 1$$?

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o -\infty$$

Question 13

A radioactive substance decays according to $$A(t) = 100 	imes 2$$^{-t/5}$$. What is the half-life of the substance?

Accepted Answer

$$5$$ units of time

Question 14

Which of the following is a rational function?

Accepted Answer

$$f(x) = \dfrac{x^2$ + 1}{x - 3}$$

Question 15

If $$\log_5$(x) = 3$$, what is $$x$$?

Accepted Answer

$$125$$

Question 16

Which of the following graphs does NOT represent a function?

Accepted Answer

A circle centered at the origin

Question 17

Given the exponential equation $$500 = 1000 	imes 2$$^{-t/4}$$, solve for t$.

Accepted Answer

$$t = 4$$

Question 18

Which property of logarithms allows you to write $$\log_B(MN) = \log_B(M) + \log_B(N)$$?

Accepted Answer

Product property

Question 19

If $$f(x) = 2x^2$ - 8x + 6$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

Question 20

A chemist measures the concentration of a substance and finds it decreases by half every 10 minutes. If the initial concentration is 80 mg/L, what is the concentration after 30 minutes?

Accepted Answer

$$10 mg/L$$

Functions, Linear and Quadratic Models, Polynomials, Exponential and Logarithmic Functions

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