Question

A bacteria culture will grow from 400 to 5000 in 1 1/4 hours.

a) Find the constant k for this bacteria using growth formula, y=ne^kt, and write the growth equation.

b)Use your equation to predict how much longer it will take the 5000 bacteria to become 15000 bacteria.

Answer 1

\[y=ne^{kt}\]

Answer 2

n is beginning

y is end

Answer 3

Correct. Dont know where to start on this problem.

Answer 4

so in beginning there was 400

Answer 5

so plug in 400 for n

Answer 6

plug in what for y?

Answer 7

5000?

Answer 8

yes

Answer 9

\[5000=400 e^{kt}\]

Answer 10

t represent time , what time do you see there

Answer 11

t would go in as 1.5

Answer 12

1 1/4= 1.25

Answer 13

I knew that.

Answer 14

let's go with that

Answer 15

k. so the equation is
\[5000=400e ^{k(1.25)}\]

Answer 16

yes

Answer 17

your job is to find k

Answer 18

Hmm...take ln of both sides and bring exponent down then solve for k?

Answer 19

exactly

Answer 20

\[\ln(5000)=k(1.25)\ln400e\]

Answer 21

not what I would do

Answer 22

How would you set it up?

Answer 23

I would divide both sides by 400 first

Answer 24

Ohh okay.

Answer 25

\[5000/400=e ^{k(1.25)}\]

Answer 26

now take ln of both sides

Answer 27

\[\ln(25/2)=k(1.25)lne\]

Answer 28

Wouldnt ln and e cancel eachother out though?

Answer 29

yes

Answer 30

So basically, to get k, you would divide ln(25/2) by 1.25?

Answer 31

yes

Answer 32

k=2.02?

Answer 33

yes

Answer 34

lol thanks. so to rewrite the equation, i would just plug everything in?

Answer 35

\[5000=400e ^{2.02(1.25)}\]

Answer 36

close but to be more general you use t instead of specific time

Answer 37

Ohh okay. So intead of 1.25, just t?

Answer 38

\[y=400e ^{2.02(t)}\]

Answer 39

that way you can find y for any t value you plug in

Answer 40

So on b, you would plug n as 5000 and y as 1500?

Answer 41

*15000

Answer 42

exactly , this time you are finding the 't'

Answer 43

I got 0.5438

Answer 44

Because you divide by 5000 on both sides.
Getting:
\[\ln(3)=(2.02)\ln(e)\]

Answer 45

And then divide by ln(2.02)
Did I do it right?

Answer 46

yes

Answer 47

Thank God. lol. But would that be like 5 mins?

Answer 48

what?

Answer 49

.5438

Answer 50

yes ,

Answer 51

it will take .5438 hours

Answer 52

okie dokes.

Answer 53

Thanks youuuu!!

Answer 54

nice to meet you

Answer 55

Nice to meet you too. It was good working with you.