Here given, initial population of bacteria = 2000 cells
Also given, the population increases at a rate of 40% per hour.
As the population is increasing so we will use the formula for exponential growth. The formula is [tex] A = Pe^{(rt)} [/tex]
Where, P = initial amount, r = growth rate, t = time, A = final amount.
So here, P = 2000, r = 40% = [tex] \frac{40}{100} = 0.4 [/tex], t = time in hours
We will plug in the values in the formula. we will get,
[tex] A = 2000e^{(0.4t)} [/tex]
We have got the required function to model the growth of the bacteria.
The required function is [tex] A = 2000e^{(0.4t)} [/tex]
