Question

find the solution to dT-k(T+45)dt=0 that satisfies T(0)=200

Answer 1

looks separable to me

Answer 2

\[\frac{1}{T+45}\ dT=-k\ dt\]

Answer 3

but without the -

Answer 4

drop an integration on it to get:
\[ln(T+45)=kt + C\]

Answer 5

how do I continue?

Answer 6

"e" it up and isolate for T

Answer 7

im not sure how well that k is going to play tho; but since t = 0 we can assume its not really a factor in the overall scheme

Answer 8

and then how do i finish and find T(0)=200

Answer 9

well, after you isolate the T; you make t=0 and solve for C

Answer 10

t=0 and T=200 that is

Answer 11

you might be able to play it as is; but lns tend to get persnickety