Question

9. The table of values represents the number of bacteria in a culture every 20 minutes.

How much greater is the average rate of change over the interval [40, 60] than the
interval [0,20]?
Time
Number of bacteria
0
100
20
200
40
400
60
800

Answer 1

• (0,100)
• (20,200)
• (40,400)
• (60,800)

For [0,20]

Average rate of change

• 200-100/20=100/20=5

for [40,60]

• (800-400)/60-40
• 400/20
• 20

Difference

• 20-5=15

Answer 2

15

Explanation:

Average rate of change over interval [40, 60] :

• A(x) = f(60) - f(40) / 60 - 40
• A(x) = 800 - 400 / 20
• A(x) = 400 / 20
• A(x) = 20

Average rate of change over interval [0, 20] :

• A(x) = f(20) - f(0) / 20 - 0
• A(x) = 200 - 100 / 20
• A(x) = 100 / 20
• A(x) = 5

Change in interval :

• 20 - 5
• 15