In 2016 Justins Alveras company had 60 fast food locations I

In 2016 Justin’s Alvera’s company had 60 fast food locations. If the company expects to grow by 15% per year, a) Write an exponential model for the number of restaurants x years after 2016 b) Use your model to predict the year when the number of restaurants will exceed 150. (As with all questions, use algebra)

Solution

a) No = 60

        r = 0.15

    Then   N(x) = No*(1 + r)^x = 60*(1 + 0.15)^x

            N(x) = 60*1.15^x

b) 150 = 60*1.15^x

      150/60 = 1.15^x

      2.5 = 1.15^x

      ln2.5 = x*ln1.15

      x = ln2.5/ln1.15 = 6.6 years