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Grace [21]
3 years ago
10

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

Mathematics
1 answer:
vitfil [10]3 years ago
6 0
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:

<span>dy/dt = 4y 
dy/4y = dt
(integral) dy/4y = (integral) dt
(1/4) ln(y) + C = t

To determine C, we substitute </span><span>y(2)=400
(1/4) ln(400) + C = 2
C = 0.5

</span><span>Find y(7).
</span>(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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