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Mathematics
Madalyn Acevedo
26 September, 12:52
Given dy/dt=4y and y (2) = 400. Find y (7).
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Pablo Koch
26 September, 13:36
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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
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