Question

Vanessa collected Barbie dolls. She began with 4 dolls and added the same amount of dolls to her collection each year. In the 24th year, Vanessa had 196 dolls. Which function, d(n), can be used to determine the number of dolls Vanessa had in any year? d(n) = 8n - 4 d(n) = 4n + 48 d(n) = 8n + 4 d(n) = 4n - 48

Answer 1

Answer:

d(n) = 8n - 4

Explanations:

Let the initial number of dolls be represented by a

She began with 4 dolls

a = 4

Let the number of years be represented by n

The 24th years means that n = 24

She added the same amount of dolls to her collection each year

The common difference is d

The number of dolls in the 24th year is 196

d(24) = 196

This is an Arithmetic Progression (AP)

The nth term of an AP is given by the formula:

d(n) = a + (n - 1)d

d(24) = 4 + (24-1)d

196 = 4 + 23d

23d = 196 - 4

23d = 192

d = 192/23

d = 8.35 = 8 ( to the nearest whole number)

The function, d(n), that can be used to determine the number of dolls Vanessa had in any year

d(n) = a + (n-1)d

d(n) = 4 + (n-1)8

d(n) = 4 + 8n - 8

d(n) = 8n - 4