Question

Abby did an experiment. She started out with 200 bacteria cells. She found that the growth rate of the bacteria cells was 3.5%. Create an equation for the situation that would work for any time, x. Type your equation into Desmos to make a graph that represents her experiment.

Answer 1

The equation for the situation is an exponential equation of the form;

• P = 200·
  `e^(0.035\cdot x)`

Please find attached the graph of the exponential equation for the population growth, created with MS Excel

What is an exponential equation?; An exponential equation is one in which the argument is an index of a number or quantity.

The initial number of bacteria cells, P₀ = 200

The equation for population growth rate can be presented as follows;

P =
`P_0 * e^{r\cdot x`

Where; P is the population of the bacteria

P₀ = The initial population of the bacteria

r = The population growth rate

x = The duration of population growth

Where r = 3.5%, P₀ = 20

3.5% = 0.035

Therefore, we get;

P =
`200 * e^{0.035\cdot x`

Please find attached the graph of the above equation created with MS Excel