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?

A.

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

B.

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

C.

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

D.

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

Answer 1

Answer: D .
`N(t) = 3 + (0.25t)^3 - 8(1.06)^t`

Explanation:

Given : 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`

Then, the difference in the number of bacteria, N(t), of both the species after t hours will be :-

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

Hence, the correct answer should be : D .
`N(t) = 3 + (0.25t)^3 - 8(1.06)^t`