Question

cool down
lesson 3: representing exponential growth
cool down: mice in the forest
a group of biologists is surveying the mice population in a forest. the equation $n = 75\cdot3^t$ gives the total number of mice, $n$, $t$ years since the survey began. explain what the numbers 75 and 3 mean in this situation.
1.) 75 represents:
2.) 3 represents:

Explanation:

1. For the value 75: In the exponential growth formula $n = a \cdot b^t$, the initial value (when $t=0$) is $a$. Substituting $t=0$ gives $n=75 \cdot 3^0 = 75 \cdot 1 = 75$, so this is the starting mouse population.
2. For the value 3: In exponential growth, $b$ is the growth factor. Each year ($t$ increases by 1), the population is multiplied by 3, meaning it triples annually.

Answer:

1. 75 represents the initial number of mice in the forest when the survey began.
2. 3 represents the growth factor, meaning the mouse population triples each year.