Advanced Math: Nonlinear functions — Quiz 3

Questions in this quiz (10)

1. An ecologist models the population of a fish species with the function $$P(t)=5,000(0.8)^t$$, where $$t$$ is the number of years after the study began. Which of the following is the best interpretation of $$5,000$$ in this context?

   • $$\text{The population after }5\text{ years}$$
   • $$\text{The initial fish population}$$
   • $$\text{The yearly percent decrease}$$
   • $$\text{The population after }8\text{ years}$$

2. A right rectangular prism has a height of $$12$$ inches. The length of the base is $$x$$ inches, which is $$5$$ inches more than the width. Which function represents the volume $$V(x)$$ of the prism?

   • $$V(x)=x(x+12)(x+5)$$
   • $$V(x)=12x(x+5)$$
   • $$V(x)=12x(x-5)$$
   • $$V(x)=x(x-12)(x+5)$$

3. The equation $$y=81^{(x+1)}$$ has a $$y$$-intercept $$(r,s)$$. Which equivalent equation shows the value of $$s$$ as a coefficient?

   • $$y=81\cdot81^x$$
   • $$y=9^{(2x+2)}$$
   • $$y=\frac{1}{9}(9)^{(2x+3)}$$
   • $$y=\frac{1}{81}(81)^{(x+2)}$$

4. The function $$A(w)=8w^2$$ gives the area of a rectangle, where the length is $$8$$ times the width $$w$$. Which of the following is the best interpretation of $$A(5)=200$$?

   • $$\text{If the width is }5\text{ ft, the area is }200\text{ ft}^2$$
   • $$\text{If the width is }200\text{ ft, the length is }5\text{ ft}$$
   • $$\text{If the width is }5\text{ ft, the length is }200\text{ ft}$$
   • $$\text{If the width is }200\text{ ft, the area is }5\text{ ft}^2$$

5. Let $$f(x)=\frac{(x-c)^2+144}{2c}$$. If $$f(c)=12$$, what is the value of $$f(10)$$?

   • $$10$$
   • $$11$$
   • $$12$$
   • $$\frac{40}{3}$$

6. A rectangle has an area of $$96$$ square inches. The length is $$2$$ inches less than $$6$$ times the width. What is the width, in inches?

   • $$\frac{1+\sqrt{577}}{6}$$
   • $$\frac{\sqrt{52}}{7}$$
   • $$\frac{1-\sqrt{52}}{7}$$
   • $$\frac{1-\sqrt{57}}{7}$$

7. Which of the following functions has a maximum value? I. $$f(x)=-(2)^x+4$$ II. $$g(x)=3(5)^x$$

   • $$\text{I only}$$
   • $$\text{II only}$$
   • $$\text{I and II}$$
   • $$\text{Neither I nor II}$$

8. The function $$y=-50x^2+600x+2,000$$ models revenue. At what value of $$x$$ is the maximum value of the function?

   • $$3$$
   • $$6$$
   • $$10$$
   • $$12$$

9. The function $$f(x)=3^{x-2}$$. What is the value of $$f(5)$$?

   • $$3$$
   • $$9$$
   • $$27$$
   • $$81$$

10. A quadratic function has zeros at $$x=-10$$ and $$x=2$$. The vertex has a $$y$$-value of $$-36$$. What is the $$x$$-coordinate of the vertex?

    • -4