Money invested in an account that compounds interest continu

Money invested in an account that compounds interest continuously at a rate of 7 % a year is modeled by Upper A equals Upper A Subscript 0 Baseline left-parenthesis e Superscript 0.07 t Baseline right-parenthesis, where Upper A is the amount in the investment after t years and Upper A Subscript 0 is the initial investment. How long will it takethe initial investment to triple? Round your answer to one decimal place.

Solution

A=A₀e^0.07t

Let initially be x and after t years it becomes 3x

3x=x * e^.07t

3= e^.07t

taking ln on both sides

ln 3=.07t

t=ln3/.07

t=15.7 yrs