Question
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?
Answers
GPT-4o mini
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.
\[
\text{Number of periods} = \frac{36 \text{ years}}{12 \text{ years/period}} = 3 \text{ periods}
\]
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.