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?

If you know that the crop will be completely infected after 6 months and the area infected doubles each month, you can work backwards. So picture the 6th month as 100%. Then, basically divide that percentage by 2 until you reach 1/8, or .125, or 12.5. So 100% (month 6) > 50% (month 5) > 25% (month 4) > 12.5% (month 3). So 12.5% is equal to 1/8 or .125, which is what you are trying to look for.

Hope this helps!

tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-25T13:33:17+02:00

The non-food crop will be infected by one-eighth of the crop after 3 months.

What is the sum of n terms in a geometric sequence?

The sum of n terms of a geometric sequence is given by the formula,

Sn = [a(1 - r^n)]/(1 - r)

Where r - a common ratio

a - first term

n - nth term

Sn - the sum of n terms

Calculation:

Given that,

The crop is infected by pests.

The area infected doubles after each month. So, it forms a geometric progression or sequence.

The entire crop is infected after six months.

So, n = 6, r = 2(double) and consider a = x

Then the area of the infected crop after 6 months is,

S(6) = [x(1 - 2^6)]/(1 - 2)

= x(1 - 64)/(-1)

= -x(-63)

= 63x

So, after six months the area of the infected crop is about 63x

So, the one-eighth of the crop = 63x/8 = 7.875x

For one month the infected area = x (< one-eighth)

For two months it will be x + 2x = 3x (< one-eighth)

For three months it will be x + 2x + 4x = 7x ( < one-eighth)

For four months it will be x + 2x + 4x + 8x = 15x (> one-eighth)

So, the one-eighth of the crop will be infected after 3 months.

Learn more about the sum of geometric sequences here:

https://brainly.com/question/24221513

#SPJ2