enny 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?N(t) = 3 + (0.25t)3 + 8(1.06)tN(t) = 7 + (0.25t)3 + 8(1.06)tN(t) = 7 + (0.25t)3 - 8(1.06)tN(t) = 3 + (0.25t)3 - 8(1.06)t

The number of bacteria in species A at time t is given by: [tex]A(t)=5+(.25t) ^{3} [/tex].

The number of bacteria in species B at time t is given by [tex]B(t)=2+8(1.06)t[/tex]

You are asked to find N(t) which is the difference in the species at time t. Difference refers to the answer is a subtraction problem. Thus, we are asked to find N(t) = A(t)-B(t)

We subtract and obtain: [tex]N(t)=5+(.25t) ^{3}-(2+8(1.06)t )=5-2+(.25t) ^{3}-(8(1.06)t )[/tex]
That is, [tex]N(t)=3+(.25t) ^{3}-(8(1.06)t )[/tex] which is the last answer choice.

With respect to notation, it is common to denote an exponent using ^. So if we want to write [tex](.25t) ^{3} [/tex] we can write "(.25t)^3"