Question

A stable population P of mosquitoes (measured in thousands), is observed to suddenly undergo a period of acceleration, given by
a(t) = 2 − [1/(t + 4)]
after t days. If the population was initially 1000 mosquitoes, determine the function P(t), and then find the population after 21 days.
I got:
v(t)= 2t - (2)(t+4)^(1/2) + C
P(t) = t^2 - (4/3)(t+4)^(3/2) +Ct + K
K=1000
But I’m not sure how to get C

Answer 1

\[\int\limits_{}^{}a(t)=2-[\frac{ 1 }{ t+4 }]\]\[v(t)=2t-\ln(t+4) +C\] \[P(t)=t ^{2}-[(t+4)\ln(t+4)-(t+4)] +ct+k\] I think this is how the integration should go

Answer 2

it's 1/sqrt(t+4)

Answer 3

And I still need to find c

Answer 4

sorry