Answer to Question #349161 in Differential Equations for cookies

Question #349161

Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already 5 million of them. If the bacterial population follows a law of natural growth, how many bacteria should be present in the Petri dish after 5 minutes?


1
Expert's answer
2022-06-09T08:08:34-0400

Population grows according to the function


"P(t)=P(0)e^{kt}"

Given


"P(0)=1000000"

"P(2)=5000000"

Substitute


"5000000=1000000e^{k(2)}"

"e^k=\\sqrt{5}"

"P(t)=1000000(\\sqrt{5})^t"

"P(5)=1000000(\\sqrt{5})^5"

"P(5)=1000000(5\\sqrt{5})"

"P(5)=11180340"

11180340 bacteria should be present in the Petri dish after 5 minutes.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
APPROVED BY CLIENTS