Question

I am stuck on this question. Could someone work it out. Id appreciate it.

Find the amount of A in an account after t years given the following conditions.

dA/dt = 0.04A
A(0) = 7000

A(t) =

Answer 1

What is happening?

Answer 2

dA/dt = 0.04A
Separate the variables:
dA/A = 0.04dt
Integrate both sides
ln(A)=0.04t + C'
A=Ce^(0.04t)
Substitute A(0)=7000 [i.e. t=0,A=7000]
7000=C*1
or
C=7000

Therefore
A = 7000e^(0.04t)