Answered

IDNLearn.com: Where curiosity meets clarity and questions find their answers. Discover comprehensive answers from knowledgeable members of our community, covering a wide range of topics to meet all your informational needs.

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]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.