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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 :

violettiou2020

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.

ashishdwivedilVT

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 [tex]ab^x[/tex] where [tex]b\neq 1[/tex] is called an exponential function.

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

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

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

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

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

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