Question

in 1985, there were 285 cell phone subscribers in the small town of Centerville. the number of subscribers increased by 75% per year after 1985. how many cell phone subscribers were in Centerville in 1994.

Answer 1

43,872

Explanation:

The growth of cell phone subscribers in Centerville can be modeled by an exponential function.

y = ab^x . . . . . where a = initial value, b = growth factor

The growth rate is given as 75% per year, so x will have units of years. It will be zero for the year 1985. The growth factor is ...

b = 1 + growth rate = 1 +0.75 = 1.75

Then the model is ...

y = 285·1.75^x

__

For x = 1994 -1985 = 9, the number of subscribers is modeled as ...

y = 285·1.75^9 ≈ 43,872

The model predicts 43,872 cell phone subscribers in 1994.