Advanced Math: Nonlinear functions — Quiz 5

Questions in this quiz (10)

1. For the function $$f(x)=x^3-4x^2+2x+1$$, what is the value of $$f(-2)$$?

   • $$-19$$
   • $$-15$$
   • $$15$$
   • $$19$$
   • $$-27$$

2. A company has $$1,500$$ users. Each month, the number of users increases by $$6\%$$ from the previous month. Which equation represents the number of users $$U$$ after $$m$$ months?

   • $$U=1,500(0.06)^m$$
   • $$U=1,500(1.06)^m$$
   • $$U=1,500(6)^m$$
   • $$U=1,500(1.6)^m$$

3. A ball is launched, and its height is modeled by $$y=-16(x-3)^2+256$$. Which of the following best describes the vertex?

   • $$\text{The ball reaches a maximum height of }256\text{ feet after }3\text{ seconds}$$
   • $$\text{The ball reaches a maximum height of }3\text{ feet after }256\text{ seconds}$$
   • $$\text{The ball reaches a minimum height of }256\text{ feet after }3\text{ seconds}$$
   • $$\text{The ball reaches a maximum height of }256\text{ feet after }16\text{ seconds}$$

4. The function $$f(t)=400(0.5)^{t/8}$$ models the intensity of a signal. What is the value of the signal at the surface $$(t=0)$$?

   • $$400$$
   • $$0.5$$
   • $$8$$
   • $$50$$

5. The function $$g(x)=\frac{x}{a}-6$$, where $$a<0$$. What is the product of $$g(2a)$$ and $$g(4a)$$?

   • 8

6. The area of a rectangle is $$900$$ square inches. The length is $$10$$ inches more than the width. Which equation represents this situation?

   • $$0=x^2-10x-900$$
   • $$0=x^2+10x-900$$
   • $$0=x^2-10x+900$$
   • $$0=x^2+10x+900$$

7. A collectible increases in value according to $$V(x)=100(1.05)^x$$. Which statement best interprets $$V(6)\approx134$$?

   • $$\text{After }6\text{ years, the value is about }$134$$
   • $$\text{The value increases by }$134\text{ each year}$$
   • $$\text{The original value was }$134$$
   • $$\text{After }134\text{ years, the value is }$6$$

8. The function $$f(x)=(1.21)^{x/2}$$ can be rewritten as $$f(x)=\left(1+\frac{p}{100}\right)^x$$. What is the value of $$p$$?

   • $$10$$
   • $$21$$
   • $$44$$
   • $$121$$

9. The function $$p(x)+16=x^2$$. What is the minimum value of $$p(x)$$?

   • $$-16$$
   • $$0$$
   • $$16$$
   • $$-256$$

10. The function $$f(x)=(x-4)(x+6)$$. For what value of $$x$$ does $$f(x)$$ reach its minimum?

    • -1