A population of 50 foxes in a wildlife preserve doubles in size every 13 years. The function y equals 50 times 2 Superscript x​, where x is the number of 13​-year ​periods, models the population growth. How many foxes will there be after 26 ​years?

Question

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Part 1
After 26 years there will be
  
enter your response here foxes. ​(Type a whole​ number.)

Answer 1

To find the number of foxes after 26 years using the given function \( y = 50 \times 2^{x} \), we first need to determine how many 13-year periods are in 26 years.

Since 26 years divided by 13 years per period gives us:

\[ x = \frac{26}{13} = 2 \]

Now, we can plug \( x = 2 \) into the model function:

\[ y = 50 \times 2^{2} \]

Calculating \( 2^{2} \):

\[ 2^{2} = 4 \]

Now, multiply by 50:

\[ y = 50 \times 4 = 200 \]

Therefore, after 26 years, there will be 200 foxes.