Question

an exponential growth function represents a quantity that has a constant doubling time.
a. true
b. false

Explanation:

An exponential growth function is of the form \( P(t)=P_0e^{kt} \) (or \( P(t)=P_0a^t \) with \( a > 1 \)). For a quantity with constant doubling time, we can derive that the time it takes for the quantity to double (\( T \)) satisfies \( 2P_0 = P_0e^{kT} \), so \( kT=\ln(2) \), meaning \( T=\frac{\ln(2)}{k} \) (a constant if \( k \) is constant). So exponential growth functions represent quantities with constant doubling time.

Answer:

A. True