Answered

Get personalized and accurate responses to your questions with IDNLearn.com. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

Select the correct answer.

Jenny studied the characteristics of two species of bacteria. The number of bacteria of species [tex]\(A\)[/tex], [tex]\(A(t)\)[/tex], after [tex]\(t\)[/tex] hours is represented by the function [tex]\(A(t) = 5 + (0.25t)^3\)[/tex]. The number of bacteria of species [tex]\(B\)[/tex], [tex]\(B(t)\)[/tex], after [tex]\(t\)[/tex] hours is represented by the function [tex]\(B(t) = 2 + 8(1.06)^t\)[/tex].

Which function describes the difference in the number of bacteria, [tex]\(N(t)\)[/tex], of both species after [tex]\(t\)[/tex] hours?

A. [tex]\(N(t) = 3 + (0.25t)^3 - 8(1.06)^t\)[/tex]

B. [tex]\(N(t) = 7 + (0.25t)^3 + 8(1.06)^t\)[/tex]

C. [tex]\(N(t) = 7 + (0.25t)^3 - 8(1.06)^t\)[/tex]

D. [tex]\(N(t) = 3 + (0.25t)^3 + 8(1.06)^t\)[/tex]

Sagot :

GinnyAnsweridn
To determine the difference in the number of bacteria between species [tex]\( A \)[/tex] and species [tex]\( B \)[/tex] after [tex]\( t \)[/tex] hours, we need to look at the given functions and find [tex]\( N(t) = A(t) - B(t) \)[/tex].

The given functions are:
[tex]\[ A(t) = 5 + (0.25t)^3 \][/tex]
[tex]\[ B(t) = 2 + 8(1.06)^t \][/tex]

To find [tex]\( N(t) \)[/tex], we subtract [tex]\( B(t) \)[/tex] from [tex]\( A(t) \)[/tex]:
[tex]\[ N(t) = A(t) - B(t) \][/tex]
[tex]\[ N(t) = \left( 5 + (0.25t)^3 \right) - \left( 2 + 8(1.06)^t \right) \][/tex]

Next, distribute the negative sign and combine like terms:
[tex]\[ N(t) = 5 + (0.25t)^3 - 2 - 8(1.06)^t \][/tex]
[tex]\[ N(t) = (0.25t)^3 + 5 - 2 - 8(1.06)^t \][/tex]
[tex]\[ N(t) = 3 + (0.25t)^3 - 8(1.06)^t \][/tex]

Thus, the function that describes the difference in the number of bacteria [tex]\( N(t) \)[/tex] between species [tex]\( A \)[/tex] and species [tex]\( B \)[/tex] after [tex]\( t \)[/tex] hours is:
[tex]\[ N(t) = 3 + (0.25t)^3 - 8(1.06)^t \][/tex]

Therefore, the correct answer is:
A. [tex]\( N(t) = 3 + (0.25t)^3 - 8(1.06)^t \)[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.