please help me how to find

Question

a)Find the time it takes for $6,500 to double when invested at an annual interest rate of 8%, compounded continuously.

 years  

b)Find the time it takes for $650,000 to double when invested at an annual interest rate of 8%, compounded continuously.

 years  

Answer 1

This is continuous growth which utilizes the formula y= A(e^kt) where A is initial value , k is growth constant and t = time

If the investment doubles $6500 will grow to $13000 so

13000= 6500( e^.08t)

2= e^.08t Take natural log of both sides and you get]

ln2 =.08t so t = ln2/.08= 8.66 years

Part b has the same answer