precal question

Question

How long will it take for an investment of $1000 to double in value if the interest rate is 8.5% per year, compounded continuously? (Round your answer to two decimal places.)

yr

Answer 1

Basic equation: A(t) = A₀e^rt

2000 = 1000e^(0.085t)

2 = e^(0.085t)

ln(2) = ln(e^(0.085t))

ln(2) = (0.085t)ln(e)

ln(2) = (0.085t)(1)

ln(2)/0.085 = t

0.6931471806/0.085 = t

t = 8.15 years