Part I (1) Can the Black-Scholes pricing model be used to price the American call option on a non-dividend-paying stock?

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Part I
(1) Can the Black-Scholes pricing model be used to price the
American call option on a non-dividend-paying stock? If yes,
explain. If not, what model can be used?
(2) Can the Black-Scholes pricing model be used to price the
American put option on a non-dividend-paying stock? If yes,
explain. If not, what model can be used?
Part II
Assume that a stock is due to go ex-dividend in 1.5 months. The
expected dividend is 50 cents. Consider an option on this stock
when the stock price is $30, the exercise price is $29, the
risk-free interest rate is 5% per annum, the volatility is 25% per
annum, and the time to maturity is four months. What is the price
of the option if it is a European call?