4. Under favourable conditions, the rate of change of the population of a certain bacterium is directly proportional to the size of the population. Suppose that, on a particular day at 10h30, there are 100000 bacteria and that, by 11h00, the population had doubled in size. (a) Model this phenomenon with a first order ordinary differential equation, using P to denote the population size. (b) Solve the equation in (a) and express P in terms of time t. (c) Calculate how long it will take for the population to reach 550000 bacteria.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: