Question

The table below shows the amount of money, in cents, Celine had in her savings account after different number of years:

Years 2 5 1 4 6 3
Money in cents 36 972 12 324 2,916 108


What will be the amount of money, in cents, that Celine will save in 12 years?

Answer 1

2,125,764 because every year it is multiplier by three which reaches to 2,125,764

Answer 2

Hence, Celine will save 2125764 cents in 12 years.

Explanation:

We are given a set of values or table of values as:

Years 1 2 3 4 5 6

Money 12 36 108 324 972 2,916

Hence, we could clearly see that the money is increasing as a multiple of 3 as compared to money in the previous year.

i.e in 1'st year it is 12 cents.

In second year it is:

12×3=36 cents.

in third year it is:

36×3=108 cents

and so on.

Let
`m_n` denote the money in the nth year.

So, the relation is given by:

`m_n=12* 3^(n-1)`

Hence, the money that Celine will save in 12 years is given by:

`m_(12)=12* 3^(12-1)\\\\m_(12)=12* 3^(11)\\\\m_(12)=2125764`

Hence, Celine will save 2125764 cents in 12 years.