Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: An investment of $$70 increases in value at a continuous rate of 4.2$$\%$ per year. What is its value in 4 years?

$$70 \times e$$^{0.042 \times 4}$$ \approx 83.22$$

Question 1

A ball is hit and its height in meters, $$h$$, as a function of the horizontal distance $$d (in $$meters) traveled, is given by $$h(d) = -0.04d^2$ + 0.74d + 1.8. $$What is the maximum height the ball reaches?

Accepted Answer

$$h_{max} = 8.65$$ meters

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 16x + 32$$, what is the vertex of the parabola?

Accepted Answer

$$(4, 0)$$

Question 3

Which of the following is the factored form of the quadratic function $$f(x) = x^2$ - 6x + 9$$?

Accepted Answer

$$f(x) = (x - 3)^2$

Question 4

For the exponential growth function $$f(x) = 100(1.07)^x$$, what is the percent rate of change?

Accepted Answer

$$7\%$$

Question 5

Suppose $$1500 is $$invested in an account yielding interest at a nominal rate of $$6\%$$ per year, compounded monthly. What is the effective annual yield?

Accepted Answer

$$6.17\%$$

Question 6

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 7

Order the numbers $$e, \sqrt{10}, 2^3$, 6^2$, 10^3$ from smallest to largest.

Accepted Answer

$$e, \sqrt{10}, 2^3$, 6^2$, 10^3$

Question 8

An investment of $$70 increases in value at a continuous rate of 4.2$$\%$ per year. What is its value in 4 years?

Accepted Answer

$$70 	imes e$$^{0.042 	imes 4}$$ \approx 83.22$$

Question 9

What is the value of the number $$e$$, and why is it important?

Accepted Answer

$$e \approx 2.718$$, and it is the base of natural logarithms, commonly used in continuous growth and decay models.

Question 10

Rewrite $$\log_{10} 0.001$$ using exponents.

Accepted Answer

$$\log_{10} 0.001 = -3$$

Question 11

Solve for $$x$$: $$e^{0.013x} = 100$

Accepted Answer

$$x = \frac{\ln(100)}{0.013}$$

Question 12

Convert $$Q = 10$$^{2.4t}$$ to the form Q$$ = $$ae^{kt}.$$

Accepted Answer

$$Q = e$$^{(2.4 \ln 10)t}$$

Question 13

Determine the half-life of a radioactive substance that decays at a continuous rate of $$7\%$$ per day.

Accepted Answer

$$t_{1/2} = \frac{\ln 2}{0.07} \approx 9.90$$ days

Question 14

Which of the following is the correct description of the graph of $$y = -0.25(4)^x$$?

Accepted Answer

Decreasing exponential function, reflected over the $$x-$$axis

Question 15

Given the rational function $$f(x) = \frac{2x^2$ + 1}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 16

A $$5000$$ investment earns $$6\%$$ annual interest, and a $$4000$$ investment earns $$8\%$$, both compounded continuously. When will the smaller investment catch up to the larger one?

Accepted Answer

$$t = \frac{\ln(5/4)}{0.08 - 0.06}$$

Question 17

Which of the following is the standard form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 18

If the growth factor for an exponential function is $$g = 1.25$$, what is the percent rate of change?

Accepted Answer

$$25\%$$

Precalculus Exam Review: Quadratic, Polynomial, Exponential, and Logarithmic Functions

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