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: 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

Every day, the locust population is multiplied by a factor of 0.7.

The daily rate of change in the locust population is modeled by the following function:

N(t) = N(0) * (0.7)^t

Where:

N(t) is the number of locusts remaining alive at day t

N(0) is the initial number of locusts

t is the number of days since the beginning of winter

The factor 0.7 represents the proportion of the locust population that remains alive each day.

So, on the first day, 70% of the locusts are still alive, on the second day, 70% of the remaining locusts are alive, and so on.

The daily rate of change is the slope of the function N(t).

The slope is negative because the population is decreasing over time.

The absolute value of the slope is 0.3, which means that the population is decreasing by 30% each day.

To round your answer to two decimal places, you can multiply 0.3 by 100 and then round to two decimal places.

This gives you 30.00, so the daily rate of change is 30.00%.