Question

The number of coffee shops in a certain country can be modeled by the quadratic function ​f(x)105x²+680x+4296, where​ f(x) is the number of coffee shops and x is the number of years after 2000. Complete parts a and b.

a. Find the number of coffee shops in 2006.
b. If the trend described by the model​ continues, predict the year after 2000 in which the number of coffee shops will be 21;500.

Answer 1

A. X is the number of years after 2000

2006-200 = 6 years.

Replace x with 6 and solve:

105(6)^2 + 680(6) + 4296 = 12,156

Answer for part a: 12,156

Answer for part B.
There was just over 12,000 in 6 years , to get to 21,500 would be a little over 9,000 more 9/12 = 0.75

6 years x .75 = 4.5 years

6 + 4.5 = 10.5 years round to 10 years for estimating purposes

Answer for part b: about 10 years