Math Algebra 2, Logarithms

Question

Suppose you invest $10,000 in an account that compounds interest continuously and earns 12%. Explain how to set up and calculate the time required for your initial investment to triple. Round your answer to the nearest tenth of a year. 

Answer 1

If your investment tripled you would have 30000 s0

30000= 10000 x e^.12t. Divide both sides by 10000 gives

3+ e^.12t. Take the natural of of both sides

ln3= ln e^.12t so

ln 3= .12t

t= ln3/.12

T=9.155. Rounded to nearest tenth t=9.2yrs