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 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

Answer 2

Answer:

The function N(t) is given as:

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

Step-by-step 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,