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 : [tex]y = y_0 2^{x-6}[/tex] --A
Where y is the amount after x months
[tex]y_0[/tex]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. [tex]y = \frac{1}{8} y_0[/tex] --B
On comparing A and B
[tex]y_0 2^{x-6}= \frac{1}{8} y_0[/tex]
[tex]2^{x-6}= \frac{1}{8}[/tex]
[tex]2^{x-6}= 2^{-3}[/tex]
So, x-6 = -3
x = 3
Hence One-eighth of the non-food crop will be infected after the third month.
