Question

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,
N(t), is modeled by the following function:
Nday(t) = 400 • (1.1)^t
Complete the following sentence about the rate of change in the locust population.
Round your answer to two decimal places.
The number of locusts is tripled every
weeks.

Answer 1

To determine how many weeks it takes for the number of locusts to triple, we solve the equation 3 • 400 = 400 • (1.1)^t for ‘т’ to find that it takes approximately 11.53 days, which is about 1.65 weeks.

Step-by-step explanation:

The question asks how many weeks it takes for the number of locusts to triple according to the exponential growth function N(t) = 400 • (1.1)^t, where N represents the number of locusts after t days. To find when the population triples, we must solve the equation 3 • 400 = 400 • (1.1)^t. Dividing both sides by 400 gives us 3 = (1.1)^t, and we can now use logarithms to solve for t. After calculating, we convert the days into weeks by dividing by 7.

Let's solve step-by-step:

1. 3 = (1.1)^t
2. t = log(1.1)³
3. t ≈ 11.53 days (after rounding to two decimal places)
4. Weeks = 11.53 / 7 ≈ 1.65 weeks

Thus, the number of locusts is tripled every 1.65 weeks.