A population of 50 foxes in a wildlife preserve triples in size every 13 years. The function y= 50⋅3^x​, where x is the number of ​13-year ​periods, models the population growth. How many foxes will there be after 39 ​years?

1 answer

First, we need to determine how many 13-year periods are in 39 years. Divide 39 by 13 to get 3 with a remainder of 0. This means there are three 13-year periods in 39 years.

Now we can use the function y= 50⋅3^x to find the population after three 13-year periods by plugging in x=3:

y= 50⋅3^3
y= 50⋅27
y= 1,350

Therefore, there will be 1,350 foxes in the wildlife preserve after 39 years.