Answer to Question #320390 in Calculus for koi

Question #320390

It is estimated that x months from now the population of a certain town will be increasing at the rate of 2 + 6√π‘₯ people per month. The current population is 5,000. What will be the population 9 months from now?


1
Expert's answer
2022-04-06T07:37:50-0400

Let


"\\frac{dp}{dx}=2+6\\sqrt{x}"


"dp=(2+6\\sqrt{x})dx"


Integrating both sides, we have that


"P(x)=2x+4x^{\\frac{3}{2}}+k"


at "x=0, P=5000"


"5000=2(0)+4(0)^{\\frac{3}{2}}+k"


"=>k=5000"



"P(x)=2x+4x^{\\frac{3}{2}}+5000"


When "x=9"


"P=2(9)+4(9)^{\\frac{3}{2}}+5000"


"P=18+108+5000=5126"


Hence, Population 9months from now is 5126



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
New on Blog
APPROVED BY CLIENTS