Question

A bacterial culture has an initial population of 500. If its population grows to 3000 in 8 hours, what will it be at the end of 10 hours? (Use the formula P=Ie^kt) please help.

Answer 1

Using a Casio scientific calc. too if that helps at all.

Answer 2

So, the first thing that you need to do is plug in the calues that you already have.
3000=500e^8k

Answer 3

Your goal is to figure out the value of k, so that you can later plug in a 10 into the original equation

Answer 4

Do know of or are you learning about natural logs?

Answer 5

just learning about it. Been trying to do this question for a while and i just can't get my head around it.

Answer 6

Alright, so first, you need to isolate the k. ANd, you're aware that e is a predetermined ratio, right?
3000/500=e^8k

Answer 7

Correct, yes.

Answer 8

Ah, I was trying to do it as k=(500e^8)/3000

Answer 9

Alright, so after you've moved the equation, you take the natural log of both sides, and byt the rules of exponents, can move the 8k in front of the 1 the ln e creates

Answer 10

Yeah, that would get you a completely different answer.Do you understand, or do you want to finish working it out here?

Answer 11

Would you mind? Just so i can go through it later on as well...

Answer 12

Of course. 3000/500 is 6, so:
ln 6 = 8k (1)
(ln 6)/8 = k
After that, replace k in the equation with the given variables, switch the 8 with the 10, and solve for P

Answer 13

Does that make sense?

Answer 14

ish... i'm a bit slow at this just with solving for P is all

Answer 15

Just with the look of the final calculation

Answer 16

Give me a second to compute it

Answer 17

Would it look something like ln(P)/10=k=0.223?

Answer 18

The equation, once you have k, should look like:
P = 500e^10(ln6)
You should be able to solve it, if you leave it in your calculator

Answer 19

Ahh, should be all good, thanks for you help :)

Answer 20

No problem, glad I could help