Question

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 places

b) Assuming the model remains accurate, how many million Hispanic-owned businesses will there be in 2038? Round to the hundredth.

Answer 1

f(t) = 1.22·(173/122)^(t/5)

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)

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(b) In 2038-2012 = 26 years, the value of the function is ...

f(26) = 1.22·(173/122)^(26/5) ≈ 7.50 . . . . million