Question

A culture started with 6000 bacteria after 3 hours ot grew to 7200 bacteria Predict how many bacteria will be present after 19 hours

Answer 1

72006000=1.2i.e. it increases by 20% in three hours you can model this as6000×(1.2)t3

Answer 2

19038

Explanation:

Given : A culture started with 6000 bacteria after 3 hours to grew to 7200 bacteria

To Find: Predict how many bacteria will be present after 19 hours

Solution:

General Form of exponential function:
`y=ab^x`

where y is the amount after x hours

x is the time

a is the initial amount

b is the growth factor

Bacteria initial amount= a = 6000

Time = x = 3 hours

Amount of bacteria after 3 hours = 7200

Substitute the values in the general form

`7200=6000(b)^3`

`(7200)/(6000)=(b)^3`

`\sqrt[3]{(7200)/(6000)}=b`

`1.06265856918=b`

Now we are supposed to find how many bacteria will be present after 19 hours

So, Bacteria initial amount= a = 6000

Time = x = 19 hours

Amount of bacteria after 19 hours = y

Substitute the values in the formula:

`y=6000(1.06265856918)^(19)`

`y=19038.488`

Hence there will be approximately 19038 bacteria present after 19 hours