The amounts A, B, and C, in grams, are decaying exponentially according to the functions below. Which amount will decay to 4 grams fastest?

A(t) = 8 * e^-0.1386t

B(t) = 10 * e^-0.02t

C(t) = 9 * e^-0.1t

Question

The amounts A, B, and C, in grams, are decaying exponentially according to the functions below. Which amount will decay to 4 grams fastest?

A(t) = 8 * e^-0.1386t

B(t) = 10 * e^-0.02t

C(t) = 9 * e^-0.1t

anonymous · Answer

Plug in 4 for A(t), B(t), and C(t), and algebraically solve for t using division and the natural logarithm. Whichever t is smallest is the shortest time to decay.