Question
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Part 1
A population of 50 foxes in a wildlife preserve quadruples in size every 13 years. The function y equals 50 times 4 Superscript x, where x is the number of 13-year periods, models the population growth. Using the given function, how many foxes will there be after 26 years?
Question content area bottom
Part 1
After 26 years there will be
enter your response here foxes. (Type a whole number.)
Part 1
A population of 50 foxes in a wildlife preserve quadruples in size every 13 years. The function y equals 50 times 4 Superscript x, where x is the number of 13-year periods, models the population growth. Using the given function, how many foxes will there be after 26 years?
Question content area bottom
Part 1
After 26 years there will be
enter your response here foxes. (Type a whole number.)
Answers
GPT-4o mini
To find the number of foxes after 26 years using the given function \( y = 50 \times 4^x \), we first need to determine how many 13-year periods are in 26 years.
\[
x = \frac{26 \text{ years}}{13 \text{ years/period}} = 2
\]
Now, we can substitute \( x = 2 \) into the equation:
\[
y = 50 \times 4^2
\]
Calculating \( 4^2 \):
\[
4^2 = 16
\]
Now substitute this back into the equation:
\[
y = 50 \times 16
\]
Calculating this gives:
\[
y = 800
\]
Therefore, after 26 years, there will be \(\boxed{800}\) foxes.
\[
x = \frac{26 \text{ years}}{13 \text{ years/period}} = 2
\]
Now, we can substitute \( x = 2 \) into the equation:
\[
y = 50 \times 4^2
\]
Calculating \( 4^2 \):
\[
4^2 = 16
\]
Now substitute this back into the equation:
\[
y = 50 \times 16
\]
Calculating this gives:
\[
y = 800
\]
Therefore, after 26 years, there will be \(\boxed{800}\) foxes.