Answer:
[tex]A(t) = 3500e^{0.15t}[/tex]
Step-by-step explanation:
An exponential function for the colony of bacteria has the following format:
[tex]A(t) = A(0)e^{rt}[/tex]
In which A(t) is the population after t hours, A(0) is the initial population and r is the growth rate.
There are 3,500 bacteria in the colony at the time observations begin.
This means that A(0) = 3500.
A colony of bacteria is increasing at the rate of 15% each hour.
This means that [tex]r = 0.15[/tex]
Find an exponential growth model for A, the number of bacteria t hrs after the first observation.
[tex]A(t) = A(0)e^{rt}[/tex]
[tex]A(t) = 3500e^{0.15t}[/tex]
