Question
A population of 40 foxes in a wildlife preserve triples in size every 10 years. The function y equals 40 times 3 Superscript x, where x is the number of 10-year periods, models the population growth. Using the given function, how many foxes will there be after 30 years?
Question content area bottom
Part 1
After 30 years there will be
enter your response here foxes. (Type a whole number.)
Question content area bottom
Part 1
After 30 years there will be
enter your response here foxes. (Type a whole number.)
Answers
GPT-4o mini
To determine the number of foxes after 30 years using the model given by the function \( y = 40 \times 3^x \), we first need to calculate how many 10-year periods are in 30 years.
Since 30 years corresponds to \( 30 \div 10 = 3 \) periods of 10 years, we can substitute \( x = 3 \) into the function:
\[
y = 40 \times 3^3
\]
Now we calculate \( 3^3 \):
\[
3^3 = 27
\]
Next, we multiply this by 40:
\[
y = 40 \times 27 = 1080
\]
Thus, after 30 years, there will be **1080 foxes**.
Since 30 years corresponds to \( 30 \div 10 = 3 \) periods of 10 years, we can substitute \( x = 3 \) into the function:
\[
y = 40 \times 3^3
\]
Now we calculate \( 3^3 \):
\[
3^3 = 27
\]
Next, we multiply this by 40:
\[
y = 40 \times 27 = 1080
\]
Thus, after 30 years, there will be **1080 foxes**.