Exponential growth and decay — Advanced Math

Questions in this quiz (10)

1. Which function represents exponential growth?

   • $$y=50(1.2)^x$$
   • $$y=20-2x$$
   • $$y=5x^2$$
   • $$y=100(0.8)^x$$

2. A $$500$$ investment decreases by $$12\%$$ each year. Which equation models the value after $$t$$ years?

   • $$V=500(1.12)^t$$
   • $$V=500(0.12)^t$$
   • $$V=500(0.88)^t$$
   • $$V=500(1-0.12t)$$

3. A population of bacteria doubles every 6 hours. If there are 200 bacteria initially, how many are there after 18 hours?

   • $$800$$
   • $$400$$
   • $$1600$$
   • $$3200$$

4. A radioactive element has a half-life of $$10$$ years. If you start with $$80$$ grams, how many grams remains after $$30$$ years?

   • $$40$$
   • $$20$$
   • $$5$$
   • $$10$$

5. The value of an investment grows according to $$A=1200(1+r)^5$$ and equals $$1500$$ after 5 years. What is the annual growth rate $$r$$?

   • $$0.08$$
   • $$0.10$$
   • $$0.15$$
   • $$0.046$$

6. An account is compounded annually at 4%. How much will $1000 become after 3 years?

   • $1120
   • $1124.86
   • $1140.25
   • $1300.67

7. Which function grows faster as $$x$$ increases?

   • $$f(x)=200(1.05)^x$$
   • $$g(x)=150(1.08)^x$$
   • $$f$$ and $$g$$ grow at the same rate
   • Cannot be determined

8. On a graph of $$y=a(1.3)^x$$ what happens when $$x$$ increases by $$1$$?

   • The $$y$$-value increases by 1.3 times
   • The $$y$$-value increases by 0.3
   • The $$y$$-value decreases by 30%
   • The graph shifts upward by 1.3 units

9. The function $$y=200(1.25)^t$$ models a population. After how many years will the population reach $$y=625$$?

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

10. A medicine decays continuously according to $$A=A_0e^{-0.3t}$$. What fraction of the medicine remains after 5 hours?

    • $$e^{-1.5}$$
    • $$e^{1.5}$$
    • $$0.3e^5$$
    • $$e^{-0.5}$$