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On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts remaining alive in this population decreases rapidly due to the lack of flowers for them to eat. The relationship between the elapsed time, ttt, in days, since the beginning of winter, and the total number of locusts, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function: N(t)=8950⋅(0.7)2t Complete the following sentence about the daily percent change of the locust population. Round your answer to the nearest percent. Every day, there is a \%%percent the locust population.

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Answer:

Every day, there is a 49% percent the locust population.

Step-by-step explanation:

To find the daily percent change of the locust population, we just need to find N(t) for t = 0, N(t) for t = 1, then subtract the second by the first, and then divide the result by the first:

N(t) = 8950*(0.7)^2t

N(0) = 8950*(0.7)^0 = 8950*1 = 8950

N(1) = 8950*(0.7)^2 = 8950*0.49 = 4385.5

Change = N(1) - N(0) = 4564.5

Percent change = Change/N(0) = 4564.5/8950 = 0.51 = 51%

As after one day, the population decrease by 51% of the inicial population, the remaining population is 100% - 51% = 49%, so we can write:

Every day, there is a 49% percent of the locust population.

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