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

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Mathematics

Butterscotch

2 February, 08:52

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

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Sam · 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.