Question

a culture started with 2000 bacteria. After 4 hours, it grew to 2600 bacteria. Predict how many bacteria will be present after 17 hours

Answer 1

`P = 6099\ bacterias`

Explanation:

We must use the exponential growth formula:

`P = be ^ {rt}`

Where

P is the population of bacteria as a function of time

b is the initial population of bacteria.

r is the growth rate

t is the time in hours

We know that the initial amount of bacteria is 2000. Then
`b = 2000`

Then

`P = 2000e ^ {rt}`

After t = 4 hours the population P was 2600. Then we substitute these values in the equation and solve for r.

`P = 2600 = 2000e^(4r)`

`(2600)/(2000) = e ^ {4r}`

`1.3 = e ^ {4r}\\\\ln (1.3) = ln (e ^ {4r})\\\\ln (1.3) = 4r\\\\r = (ln (1.3))/(4)\\\\r = 0.06559`

Now we can write the equation for this problem as:

`P = 2000e ^(0.06559t)`

For t = 17 hours the amount of bacteria will be:

`P = 2000e ^(0.06559 (17))`

`P = 6099\ bacterias`