Question

You complete 3 centimeters of a necklace in an hour. each hour after the first, you triple the length iof the necklace. write an expression using the exponents for the length of the necklace after 3 hours. then find the length

Answer 1

`L_n=3^n`

Length after 3 hours = 27 centimeters

Explanation:

Let us solve this while making a table

Hours(n) Length (L)

1 3

2 3 x 3 = 9 =
`3^2`

3 9 x 3 = 27 =
`3^3`

4 27 x 3 = 81 =
`3^4`

n
`3^n`

Hence we can draw an expresssion as

`L_n = 3^n`

to measure the length of the necklace after n hours.

Hence

`L_3=3^3`

`L_3=27`

Answer 2

First hour: 3 = 3¹

Second hour: (3) x 3 = 3²

Third hour: (3 x 3) x 3 = 3³

Fourth hour: (3 x 3 x 3) x 3 = 3⁴

Do you see the pattern?
`3^(n)` where n is the number of hours

Answer: 3³,
`3^(n)`