Respuesta :

sqdancefan

This is a separable differential equation so can be written as

[tex]\dfrac{dA}{A}=0.02\,dt[/tex]


Integrating, then taking antilogs, you have

[tex]\displaystyle\int{\frac{dA}{A}}=0.02\int{dt}\\\\\ln(A)+C=0.02t\\\\A=C\cdot e^{0.02t}[/tex]


The exponential factor is 1 at t=0, so the multiplying constant is 4000.

[tex]A=4000e^{0.02t}[/tex]

dA/dt = 0.02A


dA/A = 0.02dt


integrating left n right


lnA = 0.02t + C where C is a constant


at t=0, A=4000


C=ln4000


lnA = 0.02t + ln4000


0.02t = lnA-ln4000


t = ln(A/4000) / 0.02


t = 40ln(A/4000)


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