Question

A nest of ants initially contains 500 individuals. The population is increasing by 12% each week.

a) How many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)How many weeks will it take for the ant population to reach 2000.

Answer 1

A)4, 823
B)13 Weeks

A: 500 (1 + .12)^x (which is 500 (1 + .12)^20 now)
= 4823. 15 which is ≈ 4823.

B: 2000/ y1 = 500 (1 + .12)^x / y2

12.23 so 13 weeks

Answer 2

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

`A=P(1+r)^x`

`\implies A=500(1+0.12)^x=500(1.12)^x`

a) (i) If x = 10 weeks,

The number of ants would be,

`A=500(1.12)^(10)=1552.92\approx 1553`

(ii) If x = 20 weeks,

The number of ants would be,

`A=500(1.12)^(20)=4823.15\approx 4823`

b) If A = 2000

`\implies 2000 = 500(1.12)^x`

`4=(1.12)^x`

Taking log both sides,

log(4) = xlog(1.12)

⇒ x = 12.23 ≈ 12 weeks