Question

On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population gains 6/7 of its size every 2.4 days, and can be modeled by a function, L, which depends on the amount of time, t (in days). Before the first day of spring, there were 4600 locusts in the population. Write a function that models the locust population t days since the first day of spring.

Answer 1

Answer:

4600*(13/7)^t/2.4.

Step-by-step explanation:

We already know that it starts with 4600 locusts. You may think we just do: 4600*6/7. But notice they said: "Of it's size" So it would actually be; 4600+4600*6/7. We can take out a 4600 to make it: 4600(1+6/7). 1 AKA 7/7+6/7 is 13/7. Now we have: 4600*13/7. The problem also says:" Every 2.4 days". Lastly, we add an exponent to 13/7 as t/2.4 days. Our final answer is 4600*(13/7)^t/2.4.

Answer 2

The function that models the locust population t days since the first day of spring was derived.

Initial population=4600

The locust population gains 6/7 of its size every 2.4 days means it has exponential growth.

What is an exponential function?

Any function of the form $ab^x$ where $b\neq 1$ is called an exponential function.

This means in 2.4 days it becomes (1+6/7) =$4600(13/7)^1*$

In 2.4*2 days it will become = $4600(13/7)^2$

Similarly, In 2.4*t days it will become =  $4600(13/7)^t$

So, in 't' days it will become = $4600(13/7)^\frac{t}{2.4}$

Thus, the function that models the locust population t days since the first day of spring was derived.

To get more about exponential functions visit:

https://brainly.com/question/2456547