Question

a scientist investigating a new type of bacteria has created the following model for the population of bacteria: p(t)=120e^t, where t is the number of days. what does 120 represent in this context? rate of bacteria growth

Explanation:

Step1: Recall exponential - growth formula form

The general form of an exponential - growth model for population is $P(t)=P_0e^{kt}$ or $P(t) = P_0a^{t}$, where $P_0$ is the initial population, $k$ is the growth constant, $a$ is the base of the exponential function, and $t$ is time. In the given function $P(t)=120e^{kt}$, when $t = 0$, $P(0)=120e^{k\times0}=120$.

Step2: Determine the meaning of the constant

Since when $t = 0$ (the starting time), the population of bacteria $P(0)=120$, the number 120 represents the initial population of bacteria.

Answer:

Initial population of bacteria