Given dy/dt=4y and y(2)=450. Find y(8).

Answer 1

dy/dt = 4y
dy/y = 4 dt
lny = 4t+ln(c)
y = c*e^(4t)
y(2)=450, so
c*e^2 = 450
c = 450/e^2 ≈ 60.9

y = 60.9 e^(4t)

so, now find y(8)

Answer 2

I keep getting some huge number when I do 60.9(e^(4*8)) and I know that's not right..

Answer 3

Let me recheck Steves response
lny = 4t+ln(c)
y = ke^4t
y(2)=450, so
c*e^8 = 450 Here is where I change to my work.
c = 450/e^8 ≈ 2981

y = 2981 e^(4t)

y(8)=2981e^16=2.64e10

Answer 4

Good call. I forgot the 4t
But 450/e^8 = 0.15

The answer is still big, though.