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.

Answer 1

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.

Answer 2

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