Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is represented by the function, A(t) = 5 + (0.25t)3. The number of bacteria of species B, B(t), after t hours is represented by the function, B(t) = 2 + 8(1.06)t. Which function describes the difference in the number of bacteria, N(t), of both the species after t hours?

We are given two functions, A(t) and B(t), and we just need to find their difference. 

The functions are [tex]A\left(t\right)=5+\left(0.25t\right)^3[/tex] and [tex]B\left(t\right)=2+8\left(1.06\right)^t[/tex].

Now, if we subtract the two functions, we have
     [tex]A\left(t\right)-B\left(t\right)=5+\left(0.25t\right)^3\:-\left(2+8\left(1.06\right)^t\right)[/tex]

     [tex]=5+\left(0.25t\right)^3\:-2-8\left(1.06\right)^t[/tex]
     
     [tex]=3+\left(0.25t\right)^3\:-8\left(1.06\right)^t[/tex]

We can not combine anything from this because there are no more like terms. Therefore, that is our final answer.