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 locust population increases by a factor of 5 every 22 days, and can be modeled by a function, L, which depends on the amount of time, t (in days).

Before the first day of spring, there were 7600 locusts in the population.
Write a function that models the locust population t days since the first day of spring.
L(t) = left parenthesis, t, right parenthesis, equals

Answer 1

The locust population can be modeled by the exponential function L(t) = 7600 * (5((t-22)/22)). The function takes into account the initial population, the growth factor of 5, and the number of 22-day periods that have passed since the start.

Step-by-step explanation:

The locust population can be modeled by an exponential function.

Since the locust population increases by a factor of 5 every 22 days, we can write the function as L(t) = 7600 * (5^((t-22)/22)).

Let's break down the function:

1. We start with the initial population of 7600 locusts.
2. The factor of 5 represents the population increasing by 5 times.
3. The exponent ((t-22)/22) represents the number of 22-day periods that have passed since the start.

Therefore, the function that models the locust population t days since the first day of spring is L(t) = 7600 * (5^((t-22)/22)).