Given the graph which shows the population of a bacteria in an experiment, measured every hour.
The graph is a graph of an exponential function.
An exponential function is given by
[tex]f(t) = a(r)^t[/tex]
where: a is the initial value of the function when t = 0,
r is the growth/decay rate, and
t is the time elapsed.
From the graph, the initial size of the population when t = 0 is 10, thus, the value of a in the function is 10.
Also, from the graph, after 2 hours, the popolation of bacteria was 20,
i.e.
[tex]20=10(r)^2 \\ \\ r^2=2 \\ \\ r= \sqrt{2} =1.4[/tex]
Therefore, the function representing the population of the bacteria after t hours is
[tex]f(t)=10(1.4)^t[/tex]
