Question

Which function represents the population of the bacteria agter t hours

Answer 1

Option A:
`f(t)=10(1.4)^(t)` is the function that represents the population of the bacteria after t hours.

Step-by-step explanation:

The graph shows the population of the bacteria for every t hours.

We shall determine the function using the formula,

`f(t)=a(b)^t`

Let us determine the value of a and b by substituting the coordinates
`(0,10)` and
`(2,20)` in the above formula.

Substituting
`(0,10)` in the formula
`f(t)=a(b)^t`, we get,

`10=a(b)^0`

`10=a`

Thus, substituting
`a=10` and
`(2,20)` in the formula, we have,

`20=10(b)^2`

`2=b^2`

`√(2) =b`

`1.4=b`

Thus, the value of a and b are
`a=10` and
`b=1.4`

Substituting these values in the formula
`f(t)=a(b)^t`, we have,

`f(t)=10(1.4)^(t)`

Thus, the function that represents the population of the bacteria after t hours is
`f(t)=10(1.4)^(t)`

Hence, Option A is the correct answer.