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 gains 6/7 of its size every 2.4 , 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 4600 locusts in the population.
Write a function that models the locust population t days since the first day of spring.

L(t) =

The population of locusts gains 47% of its size every    4.8     days.

Explanation:

Just for better understanding, deleting the typos and arranging the garbled function, the text is:

The relationship between the elapsed time t, in days, since the beginning of spring, and the number of locusts, L(t), is modeled by the following function:

Analyze each part of the function:

L(t) is the number of locusts (given)

990 is the initial value of the function, when t = 0 because, when t = 0 (1.47)⁰ = 1 and L(0) = 990.

1.47 is the growing factor: 1.47 = 1 + 0.47 = 1 + 47%. Thus, the growing factor is 47%.

t is the the elapsed time in days (given): number of days since the spring began.

The power, t/4.8, is the number of times the growing factor is applied to (mulitplied by) the initial number of locusts. If the number of days is 4.8 then t/4.8 = 4.8/4.8 = 1, meaning that the polulations of locusts grows 47% every 4.8 days.

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