Question

The revenue of Apple® went from $54.5 billion in 2013 to $74.6 billion1 in 2015. Find an exponential function to model the revenue as a function of years since 2013. What is the continuous percent growth rate, per year, of revenue?
(I have the percent rate, I need the exponential equation in Ae^kt form! )

Answer 1

r = continuous growth rate

revenue t years after 2013 = 54.5×10⁹×e^(rt)

74.6×10⁹ = 54.5×10⁹×e^(2r)

e^(2r) = 74.6/54.5

2r = ln(74.6/54.5)

r = ½ln(74.6/54.5) ≅ 0.15697 = 15.697% per year

Hope this helps!