Question

On the first day of spring, an ențire 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, Nday (t), is modeled by the following function: Nday (t) = 300.(1.2)^t

Complete the following sentence about the weekly rate of change in the locust population.
Round your answer to two decimal places.
Every week, the number of locusts grows by a factor of

Answer 1

3.58

Explanation:

You want to know the weekly growth factor if the daily growth factor is 1.2.

7 days

The weekly growth factor will be the growth factor over 7 days:

(1.2)^7 ≈ 3.58

Every week, the number of locusts grows by a factor of 3.58.

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Additional comment

The exponential model is ...

number = (initial number)(growth factor)^t

The period of time associated with the growth factor is the units associated with t. Since 1 week = 7 days, the multiplier for 7 days is ...

weekly growth factor = (daily growth factor)^7

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