Section I Part B — Full Practice Exam 3

Questions in this quiz (11)

1. Solve the logarithmic inequality $$\log_2(x-5)+\log_2(x-1)\le3$$

   • $$[3-2\sqrt{3},1)\cup(5,3+2\sqrt{3}]$$
   • $$1<x\le5+\sqrt{17}$$
   • $$5<x<3+2\sqrt{3}$$
   • $$x\le3+2\sqrt{3}$$

2. The function $$f(x)=3^{-\frac{x}{3}}\sin\left(\frac{\pi x}{3}\right)$$ represents a sound wave. What is the average rate of change of $$f(x)$$ over the interval $$[-3,3]$$ to the nearest hundredth?

   • $$-0.53$$
   • $$0$$
   • $$0.48$$
   • $$0.53$$

3. At what value of $$x$$ does the absolute minimum of $$g(x)=e^{0.8x}\cos(x)$$ occur over the interval $$[0,2\pi]$$?

   • $$0$$
   • $$\pi$$
   • $$\frac{\pi}{2}$$
   • $$2\pi$$

4. What is the solution to $$x^3-6x^2-15x+54$$>$$0$$?

   • $$(-3,3)\cup(6,\infty)$$
   • $$(-\infty,-3)\cup(3,6)$$
   • $$(-3,3)$$
   • $$(3,6)$$

5. If $$y=\frac{ax+b}{cx+d}$$ has a horizontal asymptote $$y=3$$ and a vertical asymptote at $$x=-2$$, and $$c=2$$, what is the value of $$a+d$$?

   • $$2$$
   • $$5$$
   • $$8$$
   • $$10$$

6. The profit for a company is modeled by $$P(t)=12t^2+18t+450,$$ where $$t$$ is the number of years since $$2005$$ and $$P(t)$$ is in thousands of dollars. If this trend continues, in what year will the company's profit be $$600{,}000$$?

   • $$2007$$
   • $$2008$$
   • $$2009$$
   • $$2010$$

7. A radioactive substance has a half-life of $$40$$ days. If an experiment begins with $$250$$ grams of the substance, which equation approximates the amount $$A$$ of the substance after $$t$$ days?

   • $$A=250(0.98)^t$$
   • $$A=250(0.5)^{40t}$$
   • $$A=250\left(\frac{1}{80}\right)^t$$
   • $$A=250(1.017179)^t$$

8. The heights of consecutive bounces of a ball form a geometric sequence. The height of the second bounce is $$96$$ inches, and the height of the fourth bounce is $$24$$ inches. To the nearest inch, what is the height of the sixth bounce?

   • $$12$$
   • $$10$$
   • $$8$$
   • $$6$$

9. The table below shows the pressure $$p$$, in atmospheres, at selected altitudes $$h$$, in kilometers. Which equation best represents a logarithmic model of the data?

   • $$h=-8.12\ln p+0.05$$
   • $$h=0.05-8.12p$$
   • $$h=8.12\ln p+0.05$$
   • $$h=-20.05+8.12\ln p$$

10. The function $$S(d)=450\log d+120$$ relates $$S(d)$$, the speed of a storm in miles per hour, to $$d$$, the distance it travels in miles. If the speed reaches $$570$$ mph, estimate the distance the storm can travel.

    • $$3\text{ miles}$$
    • $$10\text{ miles}$$
    • $$30\text{ miles}$$
    • $$300\text{ miles}$$

11. If $$\cos\theta=\frac{5}{13}$$ and $$0\le\theta\le\frac{\pi}{2},$$ evaluate $$\sin\theta\tan\theta.$$

    • $$\frac{144}{65}$$
    • $$\frac{144}{169}$$
    • $$\frac{12}{13}$$
    • $$\frac{5}{12}$$