Question

An exponential function for a mouse population is f(t) = 25,000(1.49)t where t is time in years. Which of the following is the correct interpretation of this function?

1) The initial mouse population is 25,000 mice. Their population increases by 49% every year.
2) The initial mouse population is 25,000 mice. Their population decreases by 49% every year.
3) The initial mouse population is 25,000 mice. Their population increases by 1.49 mice every year.
4) The initial mouse population is 25,000 mice. Their population decreases by 1.49 mice every year.

Answer 1

The correct interpretation of the function f(t) = 25,000(1.49)^t is that the initial mouse population is 25,000 and it increases by 49% every year.

Step-by-step explanation:

The exponential function provided represents the population growth of mice. It is given by f(t) = 25,000(1.49)^t where t is the time in years. Upon examining the function, the correct interpretation is that the initial population of mice is 25,000. The population then increases by 49% each year. This is because the base of the exponent, 1.49, represents a 149% total size each year, which means a 49% increase from the original size. Therefore, the initial size is 100% and with the growth, it becomes 149%, which is the 49% annual increase.