Question

Question: 3F4-b http://goo.gl/mcPV6
Answer: http://goo.gl/CdZIr

Specific Question to follow in comment.

Answer 1

My question is about the exponentiation.
We have:
\[\ln |T − Te| = −kt + c\]
which becomes:
\[T − Te = ±e^c*e^{-kt} =Ae^{-kt}\]

Why does the exponentiation not result in:
\[e^{-kt}+e^c\] on the right side, or are these equivalents?
Can someone show a breakdown of the steps involved? :/
Also: How doe does the absolute value sign become the +- on the right.

Answer 2

\[\huge e ^{-kt+C} = e ^{-kt}e ^{C}\]

Answer 3

ok, that makes sense, derived from the propoerties. What about the +-

Answer 4

Why don't we exponentiate each term separately though?

Answer 5

Cuz that's not how math works! XD lol

Answer 6

if |a| = b
a=b OR a=-b
a= \(\pm\)b