Given dy/dt=4y and y (2) = 400. Find y (7).

For us to find the value of y at t equal to 7, we need to integrate first the differential equation given above. It is a variable separable equation so we can easily integrate it as follows:

dy/dt = 4y

dy/4y = dt

(integral) dy/4y = (integral) dt

(1/4) ln (y) + C = t

To determine C, we substitute y (2) = 400

(1/4) ln (400) + C = 2

C = 0.5

Find y (7).

(1/4) ln (y) + 0.5 = t

(1/4) ln (y) + 0.5 = 7

(1/4) ln (y) = 6.5

ln (y) = 26

e^ln (y) = e^26

y = 1.96x10^11