Question

Suppose the population of a town is 5,900 and is growing 2% each year. Write an equation to model the growth in population.

Answer 1

The equation/formula to model population growth can be given below;

`\begin{gathered} P=P_0* e^(rt) \\ \text{where P = total population after time t} \\ P_0=orig\text{inal or starting population} \\ r=\text{ rate of growth in percentage} \\ t=\text{time in years} \\ e=\text{Euler's constant = }2.71828 \end{gathered}`

Therefore, for the question using the same formula, we have the model equation as;

`\begin{gathered} P_0=5000 \\ r=2\text{ \% = 2/100=0.02} \\ \text{Then the equation will be;} \\ P=5000*2.71828^(0.02t) \end{gathered}`

Hence, P = 5000 x 2.71828^0.02t