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The table shows the predicted growth of bacteria after various numbers of hours. Write an explicit formula for the number of bacteria after n hours.Hours1 2 3 4 5(n)Numberof 33 57 81 105 129BacteriaΟ Α.a= 24+9O B. a = 9n+ 24OC. a, = 24n+33OD. a = 9n +33

The Table Shows The Predicted Growth Of Bacteria After Various Numbers Of Hours Write An Explicit Formula For The Number Of Bacteria After N HoursHours1 2 3 4 5 class=

Sagot :

Let a be the number of bacteria after one hour.

From the table, we get a=33.

The difference between 57 and 33 is 57-33= 24.

The difference between 81 and 57 is 81-57=24

Hence we get the common difference d=24.

The given data is in the arithmetic progression.

The formula for the nth term in the arithmetic progression is

[tex]a_n=a+(n-1)d[/tex]

Substitute a=33 and d=24, we get

[tex]a_n=33+(n-1)24[/tex]

[tex]a_n=33+24n-24[/tex]

[tex]a_n=24n+9[/tex]

Hence the required recursive equation is

[tex]a_n=24n+9[/tex]

Option A is correct.

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