The size of the population of mosquito follows an exponential model.
the size of the population in 10 days is 1370
The size of the population in 10 days is 1370
The given parameters are:
p(0) = 574
p'(0)= 50
An exponential function is represented as:
p(t) =p(0) * e^ rt
So, we have:
p(t)=574*e^rt
Differentiate
p'(t)=574*r*e^rt
Substitute 0 for t
50=574 r
Divide both sides by 574
r=0.087
The function becomes
p(t)= 574*e^rt
= 574*e^0.087 t
In 10 days, t = 10.
So, we have:
p(10)=574*e^0.87
Solve
p(0)=1370
Hence, the size of the population in 10 days is 1370
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