Question

in exponential decay problems, the negative exponent in an expression like P(t) = 100e^(-0.173t) shows that the quantity is decreasing over time. true or false

Answer 1

True.

Reason: P(0) = 100, and for t > 0 the factor e^{-0.173t} < 1 and decreases as t increases, so P(t) gets smaller. Also P'(t) = -0.173·100 e^{-0.173t} < 0, confirming the quantity decreases.