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

Question

asked Aug 1, 2020 208k views

1 Answer

Bhavya Latha Bandaru · Answer 1 · 2020-08-06T16:12:47+0000

Answer:

$P = 6099\ bacterias$

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))

$P = 6099\ bacterias$