College Algebra

Question

There were about 1.05 million Hispanic-owned businesses in 1997 and 1.46 million in 2001.

a) Find an exponential model for this data in which t = 0 corresponds to 1997 and the number of businesses is measured in millions. $f (t) =$

b) Assuming the model remains accurate, how many million Hispanic-owned businesses will there be in 2027? million businesses

Stephen K. · Accepted Answer

Start by finding the growth rate. We know how much this increased over 4 years (1997-2001)

so 1.46 =1.05 x r^4

1.46/ 1.05 = r^4 Now take the fourth root of both sides to solve for r

r= 1.0859

So our model is f(t)= 1.05 x 1.0859^t

In 2027 t is 30 (2027-1997)

f(30) = 1.05 x 1.0859^30 = 12.4427million

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