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

Answer:

$L_n=3^n$

Length after 3 hours = 27 centimeters

Step-by-step 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, $3^{n}$