Mini Exam 3 — Timed Mini Exams

Questions in this quiz (10)

1. The table gives values for a polynomial function $$f$$ at selected values of $$x$$. What is the average rate of change of $$f$$ over the interval $$[2,5]$$?

   • $$3$$
   • $$2$$
   • $$\frac{9-3}{5-2}$$
   • $$\frac{6}{3}$$

2. A set of data is displayed on a semi-log plot where the vertical axis is logarithmic. The data points form a straight line with positive slope. Which type of function best models the data?

   • Linear
   • Exponential growth
   • Exponential decay
   • Quadratic

3. The function C models cost in dollars and is given by $$C(x)=\frac{800+bx}{x}$$. It is known that $$C(10)=90$$ and $$C(20)=50$$. What is the average rate of change of $$C$$ from $$x=40$$ to $$x=50$$?

   • $$-1$$
   • $$-2$$
   • $$-\frac{2}{5}$$
   • $$-10$$

4. The polar function is given by $$r=2+3\cos\theta$$, for $$0 \le \theta \le 2\pi$$. On which interval(s) is the distance from the origin decreasing?

   • $$(0,\pi)$$
   • $$(0,\frac{\pi}{2})$$ and $$(\frac{3\pi}{2},2\pi)$$
   • $$(\frac{\pi}{2},\frac{3\pi}{2})$$
   • $$(0,\frac{\pi}{2})$$ only

5. On a given day, the number of people, in thousands, that have entered a stadium is modeled by $$h(t)=5.12\tan^{-1}(0.6t-0.3)$$, where $$t$$ is in hours and $$0 \le t \le 10$$. Based on the model, at what time $$t$$ did person number $$3000$$ enter the stadium?

   • $$1.245$$
   • $$1.606$$
   • $$3.287$$
   • $$4.512$$

6. The function $$h$$ is given by $$h(x)=4\cdot3^x$$. For which value of $$x$$ is $$h(x)=972$$?

   • $$3$$
   • $$4$$
   • $$5$$
   • $$6$$

7. The function $$f$$ is given by $$f(x)=e^{3x}$$, and the function $$g$$ is given by $$g(x)=\ln(2x)$$ for $$x$$>$$0$$. Which of the following is an expression for $$f(g(x))$$?

   • $$2x^3$$
   • $$(2x)^3$$
   • $$e^{3\ln(2x)}$$
   • $$6x$$

8. Consider the constant function $$f(x)=2$$ and the function $$g(x)=\log_2 x$$. Let $$h(x)=g(x)-f(x)$$. In the $$xy$$-plane, what is the $$x$$-intercept of the graph of $$h$$?

   • $$(2,0)$$
   • $$(4,0)$$
   • $$(8,0)$$
   • The graph of $$h$$ does not have an $$x$$-intercept.

9. The function $$f$$ is given by $$f(x)=3^{2x}$$. Which of the following statements describes characteristics of the graph of $$f$$?

   • The graph is a vertical dilation of $$y=3^x$$, and $$f(x)=9^x$$.
   • The graph is a horizontal compression of $$y=3^x$$, and $$f(x)=9^x$$.
   • The graph is a horizontal dilation of $$y=3^x$$, and $$f(x)=9^x$$.
   • The graph is a vertical dilation of $$y=3^x$$, and $$f(x)=6^x$$.

10. For time $$t,$$ $$0\le t\le 5,$$ the rate of change of a quantity is modeled by$$P'(t)=t^3-6t^2+9t.$$At what value of $$t$$ is the quantity $$P(t)$$ maximized?

    • $$t=0$$
    • $$t=1$$
    • $$t=3$$
    • $$t=5$$