Suppose that the strike price of an American call option on a non-dividend-paying stock grows at rate

Question:

Suppose that the strike price of an American call option on a non-dividend-paying stock grows at rate g. Show that if g is less than the risk-free rate, r, it is never optimal to exercise the call early.

Strike Price
In finance, the strike price of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity.