Answer:
Step-by-step explanation:
In order to determine the equation, consider that any exponential growth equation can be written as follow:
[tex]f(t)=A(1+r)^t[/tex]
where,
f(t): amount of bacteria after t hours
A: initial amount of bacteria = 3
r: growth rate in decimal form = 0.15 (15%)
t: time in hours
By replacing the previous values into the expression for f(t) you get;
[tex]f(t)=3(1+0.15)^t\\f(t)=3(1.15)^t[/tex]
Hence, the answer is f(t) = 3(1.15)^t
Now, replace t = 13 to determine the amount of bacteria after 13 hours:
[tex]f(13)=3(1.15)^13\\f(13)=18.46[/tex]
Hence, after 13 hours there are approximately 18 bacteria