Question

a culture started with 6,000 bacteria after 6 hours it grew to 7,200 bacteria predict how much it will grow in 17 hours

Answer 1

r=0.03

A=9,991.7

Explanation:

We will use the following formula to find the rate of growth:

`A = p e^( r t )`

Here,
`A = 7200`

`P = 6000`

`T= 6 hours`

`r=((log(a)/(p) )/(log e) )/(t)`

`r=((log(7200)/(6000) )/(log e) )/(6)`

r=0.03

Now we will predict how many bacteria will be present after 17 hours using the same formula:

`A=p e^(rt)`

`A=6,000 * e^((0.03* 17))`

A=9,991.7

Answer 2

`P(t) = 10058\ bacterias`

Explanation:

To perform this calculation we must use the exponential growth formula

The exponential growth formula is

`P(t) = Ae^(kt)`

Where

A is the main coefficient and represents the initial population of bacteria

e is the base

k is the growth rate

t is time in hours.

Let's call t = 0 to the initial hour.

At t = 0 the population of bacteria was 6000

Therefore we know that:

`P(0) = 6000` bacteria

After t = 6 hours, the population of bacteria was 7200

Then
`P(6) = 7200` .

Now we use this data to find the variables a, and k.

`P(0) = 6000 =Ae ^(k(0))\\\\6000 = A(e ^ 0)\\\\A = 6000`.

Then:

`P(6) = 6000e^(k(6))\\\\7200 = 6000e ^(6k)\\\\(7200)/(6000) = e^(6k)\\\\ln((7200)/(6000)) = 6k\\\\k = (ln((7200)/(6000)))/(6)\\\\k =0.03039`

Finally the function is:

`P(t) = 6000e^(0.03039t)`

After 17 hours:

`t = 17 hours`

So the population of bacteria after t=17 hours is:

`P(t) = 6000e^(0.03039(17))`

`P(t) = 10058\ bacterias`