Question

An exterminator estimated there were 12,000 termites in a house. Each time the house was sprayed, the number of termites was reduced to one-fourth the previous number. How many termites were there after the house was sprayed x times? Write a function to represent this scenario.

Answer 1

The function governing this sit'n is a decaying exponential.

f(x) = 12000 (1/4)^x

Answer 2

`f(x)=12000*((1)/(4))^(x)`

Explanation:

Given : An exterminator estimated there were 12,000 termites in a house. Each time the house was sprayed, the number of termites was reduced to one-fourth the previous number.

To Find:How many termites were there after the house was sprayed x times? Write a function to represent this scenario.

Solution :

Since we are given that the house was sprayed x times .

Let f(x) be the no. of termites were there after the house was sprayed x times

We are also given that there are 12,000 termites in a house. Each time the house was sprayed, the number of termites was reduced to one-fourth the previous number.

Thus after spraying x times the no, of termites =

`f(x)=12000*((1)/(4))^(x)`

Thus the required function is :
`f(x)=12000*((1)/(4))^(x)`