Exponential Growth
Some real-life events grow in such a way that they can be modeled as an exponential function, given as:
[tex]C(t)=C_o(1+r)^t[/tex]Where C(t) is the future value of the measured variable, Co is its initial value, r is the growth rate and t is the time.
We are given the following data:
Initial amount: Co=40 bacteria
Growth rate: 1 + r = 3
The bacteria triples every 4 days, thus t is the number of periods of 4 days.
Thus the model is:
[tex]C(t)=40(3)^t[/tex]We can solve the equation
1 + r = 3
And get r = 2. Rewriting the equation:
[tex]C(t)=40(1+2)^t[/tex]We are required to find the number of bacteria after 20 days, that is, after 20/4 = 5 periods of 4 days. Substituting:
[tex]C(5)=40(3)^5[/tex]Calculating:
[tex]C(5)=40\cdot243=9,720[/tex]The colony would have 9,720 bacteria after 20 days