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?

Answer 1

The function N(t) is given as:

`N(t)=3+(0.25t)^3-8(1.06)^t`

Explanation:

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`

N(t) denotes the difference in the number of bacteria; hence N(t) is given by after t hours as:

N(t)=A(t)-B(t)

`N(t)= 5+(0.25t)^3-(2 + 8(1.06)^t)`

which on simplifying gives:

`N(t)=5+(0.25t)^3-2-8(1.06)^t\\\\N(t)=5-2+(0.25t)^3-8(1.06)^t\\\\N(t)=3+(0.25t)^3-8(1.06)^t`

Hence,

Answer 2

The function that describes the difference in the number of bacteria, N (t), of both species after t hours is the subtraction of the function A (t) = 5 + (0.25 t) 3 minus the function B (t) = 2 + 8 (1.06) t.
Then the function N (t) is represented by:
N (t) = A (t) - B (t)
N (t) = 3 + (0.25t) 3 - 8 (1.06) t