In Fig. 12.1 at the beginning of Chapter 12 we saw a graph showing how the rate of a calcium ATPase pump varies as a function of calcium concentration. If we extract some of the data we get the following points, where we let c denote the calcium concentration, and we let R denote the rate.

a. Use the data points at c = 0.29 and c = 0.04 to estimate R 0

(c) at c = 0.0643.

b. Similarly, estimate R 0

(c) at c = 0.29, 0.403 and c = 0.63.

c. Thus calculate R 00

(c) at c = 0.29 and c = 0.403. One of these values should be positive, the other should be negative, so we know that R 00

(c) = 0 somewhere between 0.29 and 0.403.

d. Hence estimate the value of c at which R 00

(c) = 0. (Hint:
there are a number of ways of doing this, but one simple way is to calculate the equation of the straight line between (0.29, R 00(0.29)) and (0.403, R 00(0.403)) and see where it crosses the horizontal axis.)

e. You know that R is expected to be given by the function R

(c) = 100c 2 K2 + c 2 .
Derive an expression for R 00(c). Where is R 00

(c) = 0?

f. Combine the two previous parts to estimate the value for K.
g. On the same graph, plot the data and the equation for R(c)
(using the value for K that you calculated in the previous part).