Question

Help with exponential growth

Answer 1

The number of bacteria N, in a culture is modeled by the exponential growth model, N(t) = 300e^0.025t, where t represents time in hours. According to this model, approximately how many bacteria will there be in this culture after 3 hours?

Answer 2

would this be 323?

Answer 3

Yes

Answer 4

I got 323.365

Answer 5

pls we be rounding here

Answer 6

or 323 then

Answer 7

question though for the next part it says this

Answer 8

The number of bacteria N, in a culture is modeled by the exponential growth model, N(t) = 300e^0.025t, where t represents time in hours. According to this model, estimate how many hours it will take the population of bacteria to triple.

Answer 9

so would the equation look like 3(t)=300e^0.025t

Answer 10

N(3)=300e^0.025(3)

Answer 11

ok

Answer 12

soh same answer then?

Answer 13

First, calculate the number of bacteria at t=0, then triple it.

What do you get?

Answer 14

ok one moment

Answer 15

wait its 300

Answer 16

because e^0=1

Answer 17

so 300*1=300

Answer 18

Yes, now triple it, and calculate t for that N.

Answer 19

300(3)=900

Answer 20

or

Answer 21

900 is right

Answer 22

so where would we go from there to find the time

Answer 23

\[900=300e ^{0.025t}\]

What are you gonna do 1st?

Answer 24

simplify e?

Answer 25

but we dont know what t is

Answer 26

divide both sides by 300

Answer 27

3=e^0.025(t)

Answer 28

Good, now how do you get at that exponent of e?

Answer 29

would you have to get t out of it?

Answer 30

\[lne ^{x}=x\]

Answer 31

Take the natural log of both sides

Answer 32

im confused ln3=lne^0.025t

Answer 33

or

Answer 34

Yeah, but lne^.025t = .025t

Answer 35

1.0986=.025t?

Answer 36

Yep

Answer 37

so divide both sides by .025

Answer 38

That'll work

Answer 39

4.39

Answer 40

4.43944 to be exact

Answer 41

I think you divided by .25 instead of .025

Answer 42

correct ahaha

Answer 43

44 hours

Answer 44

Your answer id 1/10 of what it should be, and watch your sig figs.

Answer 45

Yes 44 is good.

Answer 46

dang times like dis i wish i could give more than one best answer

Answer 47

Just remember - if you want to get at an exponent, take the log!