calculus
posted by trace .
assume the halflife of the substance is 31 days and the initial
amount is 183.9 grams.
(a) Fill in the right hand side of the following equation which expresses
the amount A of the substance as a function of time t (the coefficient of t in the exponent should have at least four significant digits):
(b) When will the substance be reduced to 2.4 grams?
(use decimals.)

There is not "followiong equation" to fill in.
Amount left = 183.9*2^(t/31)
You don't need 4 sig figs in the exponent in this form if the half life is exactly 31 days.
(b) When amount left = 2.4,
2.4/183.9 = 0.01088 = 2^(t/31)
4.5212 = (t/31)*ln 2 = 0.02236t
t = 202.2 days 
the second answer is 194.052 days