Question

select the correct answer. 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)=7+(0.25t)^3 - 8(1.06)^t b. n(t)=3+(0.25t)^3 + 8(1.06)^t c. n(t)=3+(0.25t)^3 - 8(1.06)^t d. n(t)=7+(0.25t)^3 + 8(1.06)^t

Explanation:

Step1: Recall the formula for difference

To find the difference $N(t)=A(t)-B(t)$. Given $A(t)=5+(0.25t)^3$ and $B(t)=2 + 8(1.06)^t$.

Step2: Calculate $A(t)-B(t)$

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

Answer:

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