Question

The rate of change in number of items sold is given by ?(?) = −31x^2 + 42x − 160⁡ thousand items per year, where x is the number of years since 1985, with data 0 ≤ x ≤ 15. Estimate the total number of items sold in 2002 and indicate whether it is extrapolation or interpolation. Use the fact that in 1990, there were 10,000 items sold.

Answer 1

We are given that rate of change in numbers is given by

x=[0,15]

Where x=Number of years since 1985

In 1990

x=5

Number of items sold=10000

Total items sold =

Total items sold=

Substitute the values

C=11566.67

In 2002

x=7

Total number of items sold in 2002

It is interpolation because x=7 lies between 0 and 15.