Question

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?

N(t) = 3 + (0.25t)3  + 8(1.06)

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

Answer 1

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

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

Now, if we subtract the two functions, we have

`A\left(t\right)-B\left(t\right)=5+\left(0.25t\right)^3\:-\left(2+8\left(1.06\right)^t\right)`


`=5+\left(0.25t\right)^3\:-2-8\left(1.06\right)^t`


`=3+\left(0.25t\right)^3\:-8\left(1.06\right)^t`

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