Exponents and exponential growth/decay Knowledge-Based Practice

Questions

1. 1.

   Two bacterial cultures grow exponentially from equal initial populations. Strain A doubles in population every 4 hours, whereas Strain B quadruples in population every 6 hours. What is the ratio of the population of Strain A to the population of Strain B after 12 hours?

   • A) $\frac{1}{2}$
   • B) $\frac{2}{3}$
   • C) $\frac{3}{4}$
   • D) $\frac{1}{4}$
2. 2.

   An invasive plant species covers an area according to the exponential growth model $A(t) = A_0 \cdot 8^{t/6}$, where $A_0$ is the initial area and $t$ is measured in weeks. After how many weeks will the area covered by the plant reach 16 times its initial area?

   • A) 8
   • B) 10
   • C) 12
   • D) 16
3. 3.

   A chemical compound decays exponentially according to the function $M(t) = M_0 \cdot (0.81)^{t/2}$, where $M_0$ is the initial mass and $t$ is measured in days. By what percentage does the mass of the compound decrease each day?

   • A) 19%
   • B) 9.5%
   • C) 90%
   • D) 10%
4. 4.

   A sample of a radioactive isotope decays exponentially according to the function $M(t) = M_0 \cdot b^t$, where $M_0$ is the initial mass, $b$ is the decay factor per hour, and $t$ is the elapsed time in hours. If an initial mass of 400 grams decays to 25 grams after 4 hours, what was the remaining mass, in grams, after 2 hours?

   • A) 50 grams
   • B) 100 grams
   • C) 200 grams
   • D) 212.5 grams
5. 5.

   A bacterial population grows exponentially according to the function $P(t) = P_0 \cdot 2^{kt}$, where $t$ is measured in hours. If the population increases from 300 to 1,200 in 6 hours, what will the population be after 15 hours?

   • A) 9,600
   • B) 4,800
   • C) 7,200
   • D) 2,550

Answers and step-by-step solutions appear after you finish the test.