Question

the table below shows the total amount spent, in billions of dollars, on tobacco products in the us.
year | spending
1987 | 35.6
1988 | 36.2
1989 | 40.5
1990 | 43.4
1991 | 45.4
1992 | 50.9
1993 | 50.5
find the average rate of change in the amount spent on tobacco products between 1987 and 1993. give units. round your answer to one decimal place. the average rate of change in the amount spent on tobacco products between 1987 and 1993 is billion dollars per year

Explanation:

Step1: Identify the formula for average rate of change

The average rate of change of a function \( y = f(x) \) between \( x = a \) and \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \). Here, \( x \) represents the year and \( f(x) \) represents the spending (in billion dollars). We need to find the average rate of change between 1987 and 1993.

For 1987 (\( x_1 = 1987 \)), the spending \( f(x_1)=35.6 \) billion dollars. For 1993 (\( x_2 = 1993 \)), the spending \( f(x_2)=50.5 \) billion dollars. The time difference \( \Delta x=x_2 - x_1=1993 - 1987 = 6 \) years.

Step2: Calculate the average rate of change

Using the formula for average rate of change:
\[
\text{Average rate of change}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{50.5 - 35.6}{1993 - 1987}
\]
First, calculate the numerator: \( 50.5-35.6 = 14.9 \)
Then, calculate the denominator: \( 1993 - 1987=6 \)
Now, divide the numerator by the denominator: \( \frac{14.9}{6}\approx2.5 \) (rounded to one decimal place)

Answer:

The average rate of change is approximately \( 2.5 \) billion dollars per year.