Question

A culture starts with 8600 bacteria. After one hour the count is 10,000.

a) Find the function that models the number of bacteria n(t) after t hours.

b) Find the number of bacteria after 2 hours.

c) After how many hours will the number of bacteria double?

Answer 1

The form of these types of equations is \[initial~amount * 1\pm~rate~of~increase=final~amount\]

Answer 2

8600*x=10,000

Answer 3

What is x (our rate of increase)?

Answer 4

e?

Answer 5

Not this time, we're just solving for x.

Answer 6

we need to put an equation together.

Answer 7

We did, 8600 * rate of change = 10000

Answer 8

So now you solve for the rate of change.

Answer 9

Well I have n(t)= 8600e^0.1508t not using X

Answer 10

That works too.

Answer 11

The answer I came up with was n(t) = 8600*(1.16279)^t

Answer 12

It seems you've got it.

Answer 13

so plug in 2 then what about c)? about doubling it?

Answer 14

Whoops, didn't see that. I'm thinking logarithms; give me a moment.

Answer 15

Sorry, I don't know if I can do that one.

Answer 16

b? or c?

Answer 17

c. With b you just plug in 2 into your equation.

Answer 18

kk! well thank you anyways

Answer 19

I know how to get it with my equation; now let me try out yours.

Answer 20

\[\ln 2 = 0.693\] e^0.693 * 8600 =our answer.

Answer 21

It's up to you to make that exponent of e in your equation equal 0.693.

Answer 22

The number of bacteria n= initial count+bt
where b is a constant
n=8600+1400t