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

Answer:

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

Step-by-step 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. $y = \frac{1}{8} y_0$  --B

On comparing A and B

$y_0 2^{x-6}= \frac{1}{8} y_0$

$2^{x-6}= \frac{1}{8}$

$2^{x-6}= 2^{-3}$

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.