Question

The function f (x) = 57.8 (1.02) x gives the approximate number of passenger cars, in millions, in the United States x years after 1960. Using this model, in about what year will the number of passenger cars reach 200 million

Answer 1

Assume this is f(x)=57.8(1.02)ˣ. This is a 2% increase each year.

When f(x)=200, 57.8(1.02)ˣ=200, (1.02)ˣ=200/57.8
Taking logs, xlog(1.02)=log(200/57.8), x= log(200/57.8)/log(1.02)=62.685.
Add 1960 to 62.685=2023 approx.