Question

A non-food crop is infected by pests on the 1st of a month. The pests infect the crop in such a way that the area infected doubles after each month. If the pests continue to infect the crop in this way, the non-food crop will be entirely infected after the sixth month.

After which month will one-eighth of the non-food crop be infected?

One-eighth of the non-food crop will be infected after the second month.
One-eighth of the non-food crop will be infected after the fifth month.
One-eighth of the non-food crop will be infected after the third month.
One-eighth of the non-food crop will be infected after the fourth month.

Answer 1

One-eighth of the non-food crop will be infected after the third month.

Explanation:

Given : A non-food crop is infected by pests on the 1st of a month. The pests infect the crop in such a way that the area infected doubles after each month.

To Find: After which month will one-eighth of the non-food crop be infected?

Solution:

Equation :
`y = y_0 2^(x-6)` --A

Where y is the amount after x months

`y_0`is the initial amount

After six months the non-food crop will be entirely infected.

Now we are supposed to find After which month will one-eighth of the non-food crop be infected i.e.
`y = (1)/(8) y_0` --B

On comparing A and B

`y_0 2^(x-6)= (1)/(8) y_0`

`2^(x-6)= (1)/(8)`

`2^(x-6)= 2^(-3)`

So, x-6 = -3

x = 3

Hence One-eighth of the non-food crop will be infected after the third month.

Answer 2

The correct answer is One-eighth of the non-food crop will be infected after the third month.