Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]

Answer 1

Answer: B) 1.6

Explanation:

`P=100e^(0.70t)\\\\\underline{\text{Substitute P = 300:}}\\300=100e^(0.70t)\\\\\\\underline{\text{Divide both sides by 100:}}\\3=e^(0.70t)\\\\\\\underline{\text{Apply ln to both sides:}}\\ln\ 3=ln\ e^(0.70t)\\\\\\\underline{\text{ln e cancels out:}}\\ln\ 3=0.70t\\\\\\\underline{\text{Divide both sides by 0.70:}}\\(ln\ 3)/(0.70)=t\\\\\\\underline{\text{Evaluate using a calculator:}}\\1.569=t`