A population of 60 foxes in a wildlife preserve quadruples in size every 12 years. The function y equals 60 times 4 Superscript x​, where x is the number of 12​-year ​periods, models the population growth. Using the given​ function, how many foxes will there be after 36 ​years?

Answer 1

To find the number of foxes after 36 years, we first need to determine how many 12-year periods are in 36 years.

\[ \text{Number of periods} = \frac{36 \text{ years}}{12 \text{ years/period}} = 3 \text{ periods} \]

Next, we will use the function \( y = 60 \times 4^x \) and substitute \( x = 3 \):

\[ y = 60 \times 4^3 \]

Now, we calculate \( 4^3 \):

\[ 4^3 = 4 \times 4 \times 4 = 64 \]

Now substituting this back into the equation:

\[ y = 60 \times 64 \]

Now, we perform the multiplication:

\[ y = 3840 \]

Thus, after 36 years, there will be 3840 foxes in the wildlife preserve.