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

So it gained 600 in 4 hours

Answer 2

600/4=150

Answer 3

It grows 150 every hour

Answer 4

sorry should have said using formula P=Ae^kt

Answer 5

150*17

Answer 6

Oh..

Answer 7

Using the data: 2000 bacteria. after 4 hours, it grew to 2600 and the formula P=Ae^kt

\(\sf 2600=(2000)e^{4k}\)

As written, P is the # of bacteria after time, t has passed, A is the initial amount, t is time and k is the rate constant.

Find the that rate constant, k is

\(k=\dfrac{ln(\dfrac{2600}{2000})}{4}=0.065591066116872775 =0.0656\)

Now use the that k to find the amount left after 17 hours

\(\large \sf P=(2000)e^{0.0656(17)}=6099.429880185858=6099\)