calculus question

Question

Find the derivative of the following function. 

A=508(1.646)^t

 

Need this to check my answer please!

Answer 1

Let y = (1.646)^t

 

Then lny = ln[(1.646)^t

 

              = tln(1.646)

 

So, y'/y = ln(1.646)

 

         y' = ln(1.646)y = ln(1.646)(1.646)^t

 

So, if A = 508(1.646)^t, then dA/dt = 508ln(1.646)(1.646)^t

 

                                                  ≈ 253.16(1.646)^t