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
