Question

A culture started with 5,000 bacteria. After 3 hours, it grew to 6,500 bacteria. How many bacteria will be present after 13 hours? Use the formula P=Ae^kt

Answer 1

5000^k*3=6500-5000=1500
5000^k=500
5000^k*(3+13)=500*16=8000
totally 5000+8000=13000 bacteria

Answer 2

er...
@marsss
\[P = Ae^{kt}\]

Answer 3

Have you learnt how to find derivatives yet?

Answer 4

@completeidiot i tried what you say but it couldn't be solved.

Answer 5

I HAVEN'T SLEPT IN TWO AND AHALF DAYS I CAN'T DO MATH, DON'T JUDGE ME.

Answer 6

nonsense
starting with the initial state

at time t=0, there is a total of 5000 cells

Answer 7

@AnImEfReaK are you a judge?

Answer 8

No just helping.

Answer 9

That's what I've been taught to do here...

Answer 10

using the equation
\[P=Ae^{kt}\]

P = the total amount of bacteria at time t
t= time lets say in hours

A and k are constants which you will need to solve for and are relatively easy to solve for given the information

now given the initial information, we can substitute the values in to get

\[5000 = Ae^{k * 0}\]

now solve for A

Answer 11

now, note that anything to the zeroth power is equal to 1, and thus the e^kt part "cancels out" or becomes one, and you will be left with A = 5000

Answer 12

@completeidiot you're really an idiot

Answer 13

now, given the 2nd set of data
after 3 hours, the total number of bacteria within the container is 6500

again using the equation

\[P=Ae^{kt}\]

since we already solve for A
and we know now that P= 6500 and t =3
we substitute those in to get

\[6500 = 5000 e^{k*3}\]

now at this point, you want to solve for k

Answer 14

@completeidiot you're wrong, can't you see?

Answer 15

THIS IS A WASTE OF TIME.

Answer 16

@marsss please kindly point out my mistake instead of concluding that i am wrong, you would be much more productive that way

Answer 17

@ughwhy_ dude, is my answer right?

Answer 18

anyways continuing on

\[6500= 5000 e^{k*3}\]
dividing both sides by 5000

\[\frac{6500}{5000} = e ^{k *3}\]

taking the natural log of both sides
\[\ln{ \frac{6500}{5000}}= 3*k\]

at this point, divide both sides by 3 to isolate k

Answer 19

since you now know k
and you also know A

you can substitute these values back into the given equation

\[P=Ae^{kt}\]

and then to determine the number of bacteria after 13 hours, make the substitution t=13 and solve for P

Answer 20

@completeidiot congratulations. you solved that like a genius

Answer 21

@UnkleRhaukus @dumbcow @.Sam.
please check my explanation/work and marsss' work

Answer 22

@completeidiot
+1