Question

on the first day of spring, an entire field of flowering trees blossoms. the population of locusts consuming these flowers rapidly increases as the trees blossom. the relationship between the elapsed time, t, in days, since the beginning of spring, and the total number of locusts, l(t), is modeled by the following function: l(t) = 750·(1.85)^t complete the following sentence about the daily rate of change of the locust population. every day, the locust population grows/shrinks by a factor of

Explanation:

Step1: Identify exponential form

The function is $L(t) = 750 \cdot (1.85)^t$, which follows the exponential growth form $L(t) = a \cdot b^t$, where $b>1$ indicates growth.

Step2: Analyze daily factor

For day $t$, $L(t)=750 \cdot (1.85)^t$. For day $t+1$, $L(t+1)=750 \cdot (1.85)^{t+1}=750 \cdot (1.85)^t \cdot 1.85 = L(t) \cdot 1.85$. This means each day the population is multiplied by 1.85.

Answer:

Every day, the locust population grows by a factor of 1.85.