A 100 capacitor is joined to a 24 V battery via a 1.0 M resistor....

The time constant of the $RC$ circuit is given by $\tau = RC = (1.0 \times 10^6 \Omega)(100 \times 10^{-6} \text{ F}) = 100 \text{ s}$.

The maximum steady-state charge on the capacitor is $Q_0 = CV = (100 \mu\text{F})(24 \text{ V}) = 2400 \mu\text{C}$.

The equation for the charge on a charging capacitor as a function of time is $q(t) = Q_0 (1 - e^{-t/\tau})$.

This equation represents an exponentially growing curve that starts from zero at $t = 0$ and asymptotically approaches the maximum charge $Q_0 = 2400 \mu\text{C}$.

Since the given time interval is $10 \text{ minutes} = 600 \text{ s} = 6\tau$, the capacitor will be nearly fully charged by the end of this period. Thus, the graph is an exponentially growing curve starting from zero and approaching $2400 \mu\text{C}$.