Mathematics > calculus > Differential Equations

Case Study - 3

A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential growth model, the rate of growth of this sample of bacteria is calculated.

The differential equation representing the growth of bacteria is given as : $\frac{dP}{dt} = kP$ where $P$ is the population of bacteria at any time '$t$'.

Based on the above information, answer the following questions :

(i) Obtain the general solution of the given differential equation and express it as an exponential function of '$t$'.