Question

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

Answer 1

Answer:

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step 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

Answer 2

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