The flux, j, of Na+

ions through a Na+

channel into a cell was measured as a function of time, t, and the following (pretend)

data were obtained.

a. Plot the data.
It’s always a good idea to look at your data first, just to get a general idea of its shape and behaviour.
By the way, setting n(0) = 0 is a scientifically stupid thing to do, as you never ever get zero Na+
in a cell, unless the cell is dead. However, let’s not worry about that for now.

b. Let n(t) denote the number of mmoles of Na in the cell, and suppose that n(0) = 0 mmol. Write an equation for n in terms of j. (Hint: we know that dn dt = j and so we just need to integrate both sides to get the desired equation. But what are the limits of integration?)

c. Estimate n(11) using a Riemann sum.

d. Just for fun, how many mmol of Na+
are there in a typical human red blood cell? 22.1 Write the general antiderivatives of the following and find a generalised formula for the antiderivative of f (x) = x r

. Are there any restrictions that must be placed on r?

a. f (x) = x 0

,

b. f (x) = x 1

,

c. f (x) = x 2

,

d. f (x) = x 3

.