There were about 1.22 million Hispanic-owned businesses in 2012 and 1.73 million in 2017.a) Find an exponential model for this data in which t = 0 corresponds to 2012 and the number of businesses is measured in millions. Round computed values to at least 4 decimal placesb) Assuming the model remains accurate, how many million Hispanic-owned businesses will there be in 2038? Round to the hundredth.
Accepted Solution
A:
Answer: f(t) = 1.22·(173/122)^(t/5)Step-by-step explanation:(a) An exponential growth (or decay) function can be written using the form ... f(t) = (initial value)·(ratio in period)^(t/period)Here, we're given an initial value of 1.22, a growth ratio of 1.73/1.22 in a period of 5 years, so we can write the function as ... f(t) = 1.22·(173/122)^(t/5)__(b) In 2038-2012 = 26 years, the value of the function is ... f(26) = 1.22·(173/122)^(26/5) ≈ 7.50 . . . . million