Question

The table shows the predicted growth of a particular bacteria after various number of hours. Write an explict formula for the sequence of the number of bacteriaA. an= 19n+19B. an= n+19C. an= 1/19nD. an=19n

Answer 1

so, we need to find the relation between hours and the number of bacteria

Let the relation is

an = m n + d

Where m and d are constants

When n = 1 , an = 19

19 = m + d eq.(1)

When n = 2 , an = 38

38 = 2m + d eq.(2)

Solve the equations (1) and (2)

subtract (1) from (2)

38 - 19 = 2m + d - ( m + d )

19 = 2m + d - m - d

19 = m

Substitute with the value of m at equation (1)

19 = 19 + d

d = 19 - 19 = 0

So, the relation will be

an = 19 n

we can check the relation

The answer is option D. an = 19 n