Question

The amounts A, B and C, in grams, are decaying exponentially according to the functions below, where t is hours. Which will decay to 3 grams faster? A(t) = 6 e-0.1733t B(t) = 8 e-0.2t C(t) = 5 e-0.11t A. Amount A B. Amount B C. Amount C

Answer 1

'Which will decay to 3 grams faster? A(t) = 6 e-0.1733t B(t) = 8 e-0.2t C(t) = 5 e-0.11t A.?"

You are dealing with exponential functions here. It's essential that you use proper notation for exponentiation. In A(t) = 6 e-0.1733t, you must use the symbol " ^ " to denote exponentation, followed by parentheses around the exponent: A(t) = 6 e^(-0.1733t). That fraction
-0.1733 is what governs the rate of decay.

You have three exponentials here, with decay constants -0.1733, -0.2 and -0.11. The magnitude of the second one: |-0.2| is greatest, so it's in Case B that the substance decays fastest.