Question

A population of 50 foxes in a wildlife preserve doubles in size every 14 years. The function y = 50.2*, where x is the number of 14-year periods, models the population

growth. How many foxes will there be after 42 years?
After 42 years there will be foxes. (Type a whole number.)

Answer 1

400

Explanation:

You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.

Periods

42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...

y = 50·2^3 = 50·8 = 400

foxes.

After 42 years, there will be 400 foxes.

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Additional comment

It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...

y = 50·2^(t/14)

Then t/14 is the number of 14-year periods when t is in years.