A population of 45 foxes in a wildlife preserve doubles in size every 15 years. The function y equals 45 times 2 Superscript x​, where x is the number of 15​-year ​periods, models the population growth. How many foxes will there be after 30 ​years?

Question

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Part 1
After 30 years there will be
  
enter your response here foxes. ​(Type a whole​ number.)

Answer 1

To find the population of foxes after 30 years, we first need to determine how many 15-year periods are in 30 years. Since 30 divided by 15 equals 2, we have \( x = 2 \).

Using the given function:

\[ y = 45 \times 2^x \]

We substitute \( x = 2 \):

\[ y = 45 \times 2^2 \]

Calculating \( 2^2 \):

\[ 2^2 = 4 \]

Now substitute that back into the equation:

\[ y = 45 \times 4 \]

Calculating \( 45 \times 4 \):

\[ y = 180 \]

Thus, after 30 years, there will be 180 foxes.