It is observed that bacteria in a certain culture doubles every hour. If 500 bacteria are present at the start of the experiment, how many will be present 3½ hours after the experiment starts?
Express the no. of bacteria f(t) present t hours after the experiment starts.
Let the rate of growth of the bacteria be r. (1 + r)^1 = 2
1 + r = 2
=> r = 1
After n hours, the number of bacteria is 2^n the initial number.
If there are 500 bacteria initially, after 3.5 hours there are 500*2^(3.5) = 500*11.313 = 5657 bacteria
As a function, the number of bacteria after time t if the initial number of bacteria is fo is given by f(t) = fo*2^t
The number of bacteria after 3.5 hours is 5657.