Question

bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria. A. Find an expression for the number of bacteria after tt hours. B. Find the number of bacteria after 5 hours. C. After how many hours will the population reach 30000

Answer 1

Answer:

A) $P = P_0 e^{rt}$

B) $19564$

C) $5.5$ or $6$ hours

Explanation:

A) The formula that can be used for bacteria after "t" hours is

$P = P_0 e^{rt}$

Where ,

$P$ represents the population after "t" hours

$P_0$ represents the initial population.

$r$ represents the rate of growth of population

$t$ represents the time taken by the population to grow

B) Here let us first find the rate of population growth.

$9000 = 400 * e^{r*4}\\3.11 = r* 4\\r = 0.778$

Thus, the population of bacteria after 5 hours

$P = 400 * e^{0.778 * 5} \\P = 400* 48.91\\P =  19564$

C)

$30000 = 400 * e^{0.778 * t) \\\\4.317 = 0.778 * t\\t = 5.549\\or t= 5.5 or 6$