Write the word or phrase that best completes each statement or answers the question.
-Use the formula $\mathrm { P } = \mathrm { Ie } \mathrm { kt }$. A bacterial culture has an initial population of 10,000 . If its population declines to 4000 in 2 hours, what will it be at the end of 4 hours?
A) 800
B) 6325
C) 3000
D) 1600

Question

Quizplus · Accepted Answer

The formula $P = Ie^{kt}$ is used to model population growth or decay, where $P$ is the final population, $I$ is the initial population, $e$ is the base of the natural logarithm, $k$ is the rate of growth or decay, and $t$ is time. Given an initial population ($I$) of 10,000 and a final population ($P$) of 4000 after 2 hours, we can solve for $k$ and then use it to find the population after 4 hours. The decline to 4000 in 2 hours indicates a decay process. Using the given information, the population at the end of 4 hours is found to be 1600, which matches option D.

Write the Word or Phrase That Best Completes Each Statement P=Iekt\mathrm { P } = \mathrm { Ie } \mathrm { kt }P=Iekt

Write the Word or Phrase That Best Completes Each Statement $\mathrm { P } = \mathrm { Ie } \mathrm { kt }$