Question

Jackelope are running rampant in Michigan. In 2010, there were 307 jackelopes, and they are increasing by 14% every year write a function rule that could be used to calculate the number of jackelopes for any number of years

Answer 1

The function rule to calculate the number of jackalopes in Michigan for any given year
`\( t \) is \( P(t) = 307 * (1 + 0.14)^t \).`

Step-by-step explanation:

This function rule represents exponential growth, where
`\( P(t) \)`denotes the number of jackalopes in Michigan after
`\( t \)`years, starting from 307 jackalopes in 2010. The term
`\( (1 + 0.14)^t \)`accounts for the 14% annual increase in the jackalope population, compounded yearly.

The initial population of 307 jackalopes serves as the starting point, and the term
`\( (1 + 0.14)^t \)`captures the continuous growth rate. The addition of 1 to 0.14 in the exponent signifies the 14% increase from year to year.

By plugging in different values of
`\( t \)`(representing years since 2010) into the function
`\( P(t) \),` one can accurately calculate the number of jackalopes in Michigan for any specific year.

This exponential growth function provides a simple and effective means to forecast the jackalope population in Michigan based on the initial count in 2010 and the yearly growth rate of 14%.