Question

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

Answer 1

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

$a_n=a+(n-1)d$

Substitute a=33 and d=24, we get

$a_n=33+(n-1)24$

$a_n=33+24n-24$

$a_n=24n+9$

Hence the required recursive equation is

$a_n=24n+9$

Option A is correct.