Q: Which piecewise-defined function models the postage $$y (in $$cents) for a letter weighing $$x$$ ounces, according to Table 3.6?

$$y = \begin{cases} 55, & 0 \u003c x \leq 1 \\ 70, & 1 \u003c x \leq 2 \\ 85, & 2 \u003c x \leq 3 \\ 100, & 3 \u003c x \leq 3.5 \end{cases}$$

Q: According to Table 3.8, what is the monthly charge for using 950 kWh of electricity?

$$C = 36.78 + 0.09398 \times (950 - 650) = 64.974$$

Question 1

Which of the following numbers is a pure imaginary number?

Accepted Answer

$$0 + 7i$$

Question 2

Given the quadratic function $$R(x) = -0.1x^2$ + 600x$$, what is the x-coordinate of the vertex?

Accepted Answer

$$x = 3000$$

Question 3

What is the domain of the function $$f(t) = 16t^2$ representing the distance an object falls from a 144-foot building?

Accepted Answer

$$t \geq 0$$

Question 4

If $$L = 2.43W$$^{0.3326}$$ models the wingspan L$ (in feet) of a bird with weight W$ (in pounds), what is the wingspan of a bird weighing 40 pounds? (Round to two decimal places)

Accepted Answer

$$L \approx 6.13$$ feet

Question 5

Which of the following best describes the graph of $$y = -0.1x^2$ + 600x$$?

Accepted Answer

A parabola opening downward

Question 6

Given the direct variation $$y = kx^n$$, if $$y = 32$$ when $$x = 2$$ and $$n = 5$$, what is the value of $$k$$?

Accepted Answer

$$k = 1$$

Question 7

Suppose the number of units of one raw material $$y$$ varies as the cube of the number of units $$x of a $$second raw material. If $$y = 500$$ when $$x = 5$$, what is $$y$$ when $$x = 10$$?

Accepted Answer

$$y = 4000$$

Question 8

Which piecewise-defined function models the postage $$y (in $$cents) for a letter weighing $$x$$ ounces, according to Table 3.6?

Accepted Answer

$$y = \begin{cases} 55, & 0 \u003c x \leq 1 \ 70, & 1 \u003c x \leq 2 \ 85, & 2 \u003c x \leq 3 \ 100, & 3 \u003c x \leq 3.5 \end{cases}$$

Question 9

According to Table 3.8, what is the monthly charge for using 950 kWh of electricity?

Accepted Answer

$$C = 36.78 + 0.09398 	imes (950 - 650) = 64.974$$

Question 10

Using Table 3.10, what is the best description of the trend in enterprise AI revenue from 2016 to 2025?

Accepted Answer

The revenue increases at an accelerating rate, suggesting a quadratic or exponential model.

Question 11

Given Table 3.11, which type of function would best model the North American cloud computing revenue data?

Accepted Answer

Quadratic function

Question 12

According to Table 3.12, what is the maximum height reached by the rocket?

Accepted Answer

$$156.8$$ meters

Question 13

Based on Table 3.14, what is the projected percent of U.S. adults with diabetes in 2040?

Accepted Answer

$$31.4\%$$

Question 14

Using Table 3.15, estimate the number of female physicians in the U.S. in 2035.

Accepted Answer

$$390,328$$

Question 15

According to Table 3.16, in what year is the purchasing power of $$1 projected to fall below 0.50$$?

Accepted Answer

2040

Question 16

If $$y$$ varies directly as the square of $$x$$ and $$y = 18$$ when $$x = 3$$, what is $$y$$ when $$x = 6$$?

Accepted Answer

$$y = 72$$

Question 17

Given the model $$y = 0.980x$$^{0.646}$$ for the percent of the U.S. population that is foreign-born, what does the exponent 0.646$ indicate about the growth?

Accepted Answer

The percent increases, but at a decreasing rate.

College Algebra Chapter 3: Quadratic, Piecewise-Defined, and Power Functions

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