For the model describing the size of a bacterial culture

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

For the model

P(t)=P_0 e^{k t}

describing the size of a bacterial culture, answer the following: (i) What does the sign of

k

indicate about the behaviour of the culture? (ii) If

k=-0.04\,\text{h}^{-1}

, interpret this value in words.