Question

The number of mold spores on a piece of bread after a different amount of time or listed in the table below

Which function models the number of mold spores on the bread after X days

Answer 1

Option (4)

Explanation:

From the table attached,

Ratio of spores in day 2 and day 1 =
`(400)/(200)`

= 2

Ratio of spores in day 3 and day 2 =
`(800)/(400)`

= 2

There is a common ratio of 2 in each successive to the previous term of the Mold spores.

Therefore, spores are growing exponentially.

Let the function representing exponential function is,

y = a(b)ˣ

Here, y = Number of spores after time 'x'

x = Number of days

a and b are the constants.

On day 1,

x = 1

y = 200

By substituting these values in the exponential function,

200 = a(b)¹

ab = 200 -------(1)

On day 2,

x = 2

y = 400

400 = a(b)² -------(2)

Divide equation 2 by equation 1,

`(400)/(200)=(ab^(2) )/(ab)`

b = 2

By substituting the value of b in equation (1),

a(2) = 200

a = 100

Therefore, equation of the function will be,

y = 100(2)ˣ

Option (4) will be the answer.