Please help me with this

Question

Write the exponential function y=40e^0.059t in the form y=ab^t. Find b accurate to four decimal places/ If t is measured in years, give the percent annual growth or decay rate and the continuous percent growth or decay rate per year.

Note: round your answers for the growth or decay rates to two decimal places.

y=

The annual rate is % per year.

The continuous rate is % per year.

Answer 1

y = 40e^0.059t=40(e^0.059)^t = 40b^t

Therefore b = e^0.059 = 1.06

y = 40(1.06)^t

_{annual rate = i = 5.9% per year}

_{Continuous rate = 12ln(1+i/12) = 0.0589 = 5.89% per year}