Q: Which of the following best describes the end behavior of $$f(x) = 5x^4$ + 5x + 11$$?

$$f(x) \to \infty as$$ $$x \to \infty$$ and $$f(x) \to \infty as$$ $$x \to -\infty$$

Q: An investor buys 100 shares of a stock for $$20,000. After 5 years, the stock is sold for 32$$,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? (Express as a percent to three decimal places.)

$$\frac{1}{5} \ln\left(\frac{32,000}{20,000}\right) \times 100 \approx 9.860\%$$

Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(-8,9), (-6,6), (5,-6), (-6,-9)\}$$

Question 2

Given $$f(x) = x^3$ - 3x + 5$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

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

Question 3

For the function $$f(x) = \sqrt{-8x-16}$$, what is the domain in interval notation?

Accepted Answer

$$(-\infty, -2]$$

Question 4

A plant can manufacture 80 golf clubs per day for a total daily cost of $$7647 and 100 golf clubs per day for a total daily cost of 9147. $$Assuming cost and production are linearly related, what is the equation for the total daily cost $$C(x) of $$producing $$x$$ golf clubs?

Accepted Answer

$$C(x) = 75x + 1647$$

Question 5

A charter fishing company buys a new boat for $$224,000 and assumes it will have a trade-in value of 115$$,200 after 16 years. What is the linear model for the depreciated value $$V of $$the boat $$t$$ years after purchase?

Accepted Answer

$$V = 224,000 - 6,800t$$

Question 6

Given the price-demand function $$p(x) = 75 - 3x$$ and the cost function $$C(x) = 125 + 16x (in $$millions of dollars), what is the revenue function $$R(x)$$?

Accepted Answer

$$R(x) = x(75 - 3x)$$

Question 7

Which of the following equations matches the graph of a cubic function?

Accepted Answer

$$y = x^3$

Question 8

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

Accepted Answer

Question 9

Convert $$\log_3$ 81 = 4 to $$exponential form.

Accepted Answer

$$3^4 = 81$

Question 10

If $$700 = 500(1.04)^x$$, what is the value of $$x$$? (Round to two decimal places)

Accepted Answer

$$x = \frac{\ln(1.4)}{\ln(1.04)}$$

Question 11

A company is introducing a new product to 2 million possible viewers. The model for the number of people $$N (in $$millions) aware after $$t$$ days is $$N = 2(1 - e$$^{-0.037t}$$). $$How many people are aware after 5 days? (Round to the nearest thousand)

Accepted Answer

$$N \approx 340,000$$

Question 12

If $$4,000 is invested at 7\%$$ compounded annually, how long will it take to grow to $$6,000$$? (Round up to the next year if not exact)

Accepted Answer

$$\frac{\ln(1.5)}{\ln(1.07)}$$

Question 13

Given $$y = (x+6)(x+7)(x+8)$$, what is the degree of the polynomial?

Accepted Answer

3

Question 14

What is the minimum number of $$x-$$intercepts a polynomial of degree 11 can have?

Accepted Answer

1

Question 15

Which of the following best describes the end behavior of $$f(x) = 5x^4$ + 5x + 11$$?

Accepted Answer

$$f(x) 	o \infty as$$ $$x 	o \infty$$ and $$f(x) 	o \infty as$$ $$x 	o -\infty$$

Question 16

Given $$C(x) = 15x + 12,000$$ and $$R(x) = 18x - 6,000$$, how many units must be produced and sold to break even?

Accepted Answer

$$6,000$$

Question 17

Which transformation sequence produces the function $$y = -6\sqrt{x} - 9$$ from the parent function $$y = \sqrt{x}$$?

Accepted Answer

Stretch vertically by 6, reflect across the x-axis, shift downward 9 units

Question 18

Solve for $$x$$: $$\ln(3x-4) = \ln 20 - \ln(x-5)$$

Accepted Answer

$$x = 6$$

Question 19

An investor buys 100 shares of a stock for $$20,000. After 5 years, the stock is sold for 32$$,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? (Express as a percent to three decimal places.)

Accepted Answer

$$\frac{1}{5} \ln\left(\frac{32,000}{20,000}ight) 	imes 100 \approx 9.860\%$$

Business Calculus Exam 1 Study Guide – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards