Question

the table below gives the annual sales (in millions of dollars) of a product.
year 1998 1999 2000 2001 2002 2003 2004 2005 2006
sales 237 264 285 300 309 312 309 300 285
determining the average rate of change of sales is important. it tells whether sales are increasing or decreasing over a time period, and at what rate.
a) what was the average rate of change of annual sales between 2001 and 2002?
9 ✔ millions of dollars/year
b) what was the average rate of change of annual sales between 2001 and 2006?
-15 × millions of dollars/year
give your answers as whole numbers.
question help: video message instructor

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) between \( x = a \) and \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \). Here, the function is sales, and the input is the year. Let \( f(t) \) be the sales in year \( t \). We need to find the average rate of change between 2001 and 2006. So, \( a = 2001 \), \( b = 2006 \), \( f(2001)=300 \) (from the table), and \( f(2006)=285 \) (from the table).

Step2: Calculate the change in sales and change in years

First, calculate \( f(b)-f(a) \): \( 285 - 300=- 15 \). Then, calculate \( b - a \): \( 2006 - 2001 = 5 \).

Step3: Compute the average rate of change

Using the formula, the average rate of change is \( \frac{-15}{5}=-3 \).

Answer:

-3