Question

Write the rule for the table.

You have three attempts to match the graph.

hours #of bacteria
1 32
2 256
3 2048
4 16384
5 131072
6 1048576

Answer 1

`A=4(8)^t`

Explanation:

Since, growth in the population of the bacteria is an exponential process,

Formula to get the population of the bacteria after 't' hours is,

`A=A_0(b)^t`

From the table given,

After 1 hour, number of bacteria = 32

32 =
`A_0(b)^1` ------- (1)

After 2 hours, number of bacteria = 256

256 =
`A_0(b)^(2)` ------ (2)

Divide equation (2) by equation (1)

`(A_0(b)^2)/(A_0(b))=(256)/(32)`

b = 8

From equation (1)

32 = 8(A₀)

A₀ = 4

Therefore, rule for the table will be,

`A=4(8)^t`