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

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

Answer 1

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.