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The table shows the predicted growth of a particular bacterium after various numbers of hours.
Write an explicit formula for the sequence of the number of bacterium.
A) an=24n+1
B) an=24n
C) an=1/24n
D) an=n+24

The table shows the predicted growth of a particular bacterium after various numbers of hours Write an explicit formula for the sequence of the number of bacter class=

Respuesta :

According with the table:
n=1→a1=24
n=2→a2=48
n=3→a3=72
n=4→a4=96
n=5→a5=120

With the first option we would get:
a1=24(1)+1=24+1→a1=25 different to 24. The equation does not work

With the second option we would get:
a1=24(1)→a1=24. The equation works
a2=24(2)→a2=48. The equation works
a3=24(3)→a3=72. The equation works
a4=24(4)→a4=96. The equation works
a5=24(5)→a5=120. The equation works

With the third option we would get:
a1=(1/24)(1)(1*1)/24→a1=1/24 different to 24. The equation does not work

With the fourth option we would get:
a1=1+24→a1=25 different to 24. The equation does not work

Answer: Second Option: an=24n
ashishdwivedilVT

An explicit formula for the sequence of the number of bacterium is [tex]a_n=24n[/tex].

Suppose the number of hours represents the x-axis while the Number of bacterium represents the y-axis.

We can represent (1,24) (2,48) (3,72) etc. on coordinate axis

Slope [tex]\frac{48-24}{2-1} =\frac{72-48}{3-2}=24[/tex]

So, there is a linear relationship between the number of hours and

the number of the bacterium.

What is the linear relationship?

If two variables are related such that they represent a straight line, they are said to be in a linear relationship.

[tex]a_n-24 = 24(n-1)\\a_n =24n[/tex]

Therefore, an explicit formula for the sequence of the number of bacterium is [tex]a_n=24n[/tex].

To get more about linear equations visit:

https://brainly.com/question/13284474

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