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