Question

Q6. A colony of ants is beg please help, I don’t know this and I have to hand it in in 20 mins

increases exponentially at a rate of 10% per week. Initially there are 500
ants.
a) Show that the number of ants in the colony forms a geometric progression
b) The number of ants in week 8 is p times greater than in week 6. Find the value of p.

Answer 1

a) The number of ants in week three is shown through the following geometric progression: 500*1.1*1.1*1.1

b) 1.21

Explanation:

We know that 500 ants are increasing at a rate of 10% every week which means that we can calculate the week one ants like this

500*1.1

Week two

500*1.1*1.1

and so on.

We write the following equation

500(1.1)^n where n is the number of weeks

We plug in 8 and then 6 for n in the equation above and get

500(1.1)^8=1071.79

500(1.1)^6=885.78

Divide and get that p=1.21