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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

Respuesta :

tramserran

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? [tex] 3^{n} [/tex] where n is the number of hours

Answer: 3³, [tex] 3^{n} [/tex]

Cricetus

Answer:

[tex]L_n=3^n[/tex]

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 = [tex]3^2[/tex]

 3                      9 x 3 = 27 = [tex]3^3[/tex]

4                       27 x 3 = 81 = [tex]3^4[/tex]

 n                     [tex]3^n[/tex]

Hence we can draw an expresssion as

[tex]L_n = 3^n[/tex]

to measure the length of the necklace after n hours.

Hence

[tex]L_3=3^3[/tex]

[tex]L_3=27[/tex]

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