The table below shows the average diameter of a pupil in a person's eye as he or she gets older.
age (years). Average Pupil Diameter (mm)
20 4.7
30 4.3
40 3.9
50 3.5
60 3.1
70 2.7
80 2.3
What is the average rate of change, in millimeters per year, of a person's pupil diameter from age 20 to 80?
ANSWER: D: -0.04
Explanation: Average rate of change is the same as slope
2.3 - 4.7/80 - 20 = -2.4/60 = -0.04
How do you think you can solve this problem?
add all the diameters divided by the sum of the ages?
Nope. The question asks for the rate of change. Note that the diameter decreased 0.4 mm every 10 years.
6 * 0.4 = _______ mm
Divide the product by 60 to find the average change per year.
Where did you get 6 from?
To find the average rate of change of a person's pupil diameter from age 20 to 80, we need to calculate the change in diameter over that time period and then divide it by the number of years.
First, let's find the change in pupil diameter:
Change in diameter = Final diameter - Initial diameter
From the given table:
Initial diameter = 4.7 mm (at age 20)
Final diameter = 2.3 mm (at age 80)
Change in diameter = 2.3 mm - 4.7 mm
Change in diameter = -2.4 mm
Next, we need to calculate the number of years:
Number of years = Final age - Initial age
Number of years = 80 years - 20 years
Number of years = 60 years
Now, we can calculate the average rate of change:
Average rate of change = Change in diameter / Number of years
Average rate of change = -2.4 mm / 60 years
Average rate of change = -0.04 mm/year
Therefore, the average rate of change of a person's pupil diameter from age 20 to 80 is -0.04 millimeters per year.