Question

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, t, in days, since the beginning of winter, and the
total number of locusts, N(t), is modeled by the following function:

N(t) 8950 (0.49)^t/2

Complete the following sentence about the daily rate of change in the locust population.
Round your answer to two decimal places.

Every day, the locust population is multiplied by a factor of ____.

Answer 1

0.7

Explanation:

Answer 2

0.70

Explanation:

You want the daily multiplier of the population, when it is described by the equation N(t) = 8950(0.49^(t/2)), where t is in days.

Multiplier

We can find the multiplier k that satisfies ...

N(1) = k·N(0)

Dividing by N(0), we have ...

k = N(1)/N(0) = (8950(0.49^(1/2)))/8950 = 0.49^(1/2) = 0.70

Every day, the locust population is multiplied by a factor of 0.70.

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