8. After you eat something containing sugar, the pH or acid level in your mouth changes. This can be modelled by the function below, where L is the pH level and n is the number of minutes that have elapsed since eating.

Question

8. After you eat something containing sugar, the pH or acid level in your mouth changes. This can be modelled by the function below, where L is the pH level and n is the number of minutes that have elapsed since eating.
L(n)= 6- 20.4n/n^2 +36

a) What is the initial pH level before you start eating?

b) Determine the average rate of change of the pH level from 2 minutes to 3.5 minutes.

c1) The average rate of change of the pH level from 3.5 to 5 minutes is approximately -0.1282/minute. Compare this to the average rate of change you calculated in.
         c2). What does this mean with respect to the given situation?

d) Estimate the instantaneous rate of change at 3 minutes. Explain what the value represents in this situation.

oobleck · Accepted Answer

I assume you meant L(n)= 6 - 20.4n/(n^2 +36) If not, then redo the calculations below
(a) L(0) = 6
(b) (L(3.5)-L(2))/(3.5-2) =
(c) look at the graph. L is decreasing, but more slowly
(d) either use a small interval such as [3,3.1] or just take the derivative to get the exact value.

Kareena · Answer

Hi can you explain to me how to do d and explain how you got b