Question

problems 8 - 9: a group of biologists tracked the number of squirrels in a town. they represented this number using the equation n = 40 • 1.5^t, where n is the total number of squirrels and t is the number of years since the biologists started counting. 8. explain what the 40 and 1.5 mean in this situation.

Explanation:

The general form of an exponential - growth equation is $n = n_0\cdot r^t$, where $n_0$ is the initial amount and $r$ is the growth factor. In the equation $n = 40\cdot1.5^t$, when $t = 0$ (at the start of counting), $n=40\cdot1.5^0=40$. So 40 represents the initial number of squirrels in the town when the biologists started counting. The number 1.5 is the growth factor. It means that the number of squirrels is multiplied by 1.5 each year, indicating a 50% growth rate per year ($1.5 = 1 + 0.5$, where 0.5 is a 50% increase).

Answer:

The 40 represents the initial number of squirrels when the biologists started counting. The 1.5 represents the growth factor, meaning the number of squirrels increases by 50% each year.