Question

A certain population of microbes grows according to the formula P = 2", where P is the size of the population and n is the number of times the population reproduces itself. If each microbe reproduces itself every 15 minutes, how large would a population of only one microbe become after five hours?

(A) 16,234,095
(B) 1,028,098
(C) 64,098
(D) 1,048,576
(E) 128,092,098

40 POINTS!!!
PLEASE HELP!!!

Answer 1

the answer is (D) 1,048,576.

Explanation:

We know that each microbe reproduces itself every 15 minutes, so in one hour (60 minutes), each microbe would reproduce itself 4 times. Therefore, in 5 hours, each microbe would reproduce itself $4\times 5 = 20$ times.

Using the formula $P=2^n$, where $n$ is the number of times the population reproduces itself, we can calculate the size of the population after 20 reproductions, starting with one microbe:

$P=2^{20} = 1,048,576$

Therefore, the population of one microbe would become 1,048,576 after 20 reproductions, or after 5 hours. So the answer is (D) 1,048,576.