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PSAT 1.17 Math Diagnostic 180 Views


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Description:

PSAT 1.17 Math Diagnostic. Which of the following functions models the number of E. coli bacteria at time h?


Transcript

00:00

Thank you We sneak And here's your shmoop du jour

00:05

brought to you by e coli Once you've gone e

00:08

coli you never go back here yet All right so

00:14

check out this info time sudden memory for people down

00:20

All right we get it Which of the following functions

00:23

models the number of e coli bacteria at time age

00:27

where h represents the number of hours since the experiment's

00:30

started And here essential answers All right the functions of

00:35

ours All right well first of all it's fine If

00:37

you want to leave e coli bacteria on the lab

00:39

table But police be sure the labeling last thing you

00:42

ever want to have happen is for some unsuspecting fellow

00:45

scientist to see the dish and mistaken for his chobani

00:48

blended plum yogurt All right well he might be spending

00:51

the next three or four hours in the emergency shower

00:53

Okay so were given a pretty simple looking table and

00:57

we're supposed to use the shadow there to assemble a

00:59

written function that represents the number of e coli bacteria

01:02

in relation to age the number of hours Well let

01:06

zero hours there in just fifteen bacteria in a petri

01:09

dish with scientists started out with every hour after that

01:13

it looks like they doubled So should be just about

01:16

four five days until they take over The world ok

01:20

well maybe we're being alarmist here but until they start

01:22

growing limbs and learn how to open and close the

01:24

door when we should be fine the good news is

01:27

that because the reign of growth is constant from one

01:30

hour to the next way no that the relationship is

01:33

exponential which means we can use this formula Why equals

01:38

eight times the quantity One plus our to the x

01:41

power well has always pays the initial amount in this

01:44

case teen bacteria our is the growth rate one hour

01:49

and x is the number of compounding period since we're

01:53

using ours is our com pounding period let's replace the

01:56

acts within age unless your friends are something in spell

02:00

ours with an x in which case well you just

02:03

keep it as is we'll also want to replace the

02:05

why of the f of age to make it more

02:08

you know function and we're left with f of h

02:11

g wells fifteen times two to the h power which

02:14

is option c if you want to double check to

02:17

make sure we set this thing up right We can't

02:19

look in any number from the time And we should

02:21

get the corresponding data in the table For example we

02:24

could plug in three thousand four hundred twenty seven hours

02:26

but we really don't want to be here all day

02:28

so instead we'll plug in five to two The fifth

02:31

power is who four eight sixteen thirty two times fifteen

02:36

which is four hundred eighty century enough consulting our table

02:40

After five hours there should be four hundred eighty bacteria

02:42

in the petri dish Option c It is all right

02:45

We've had enough of incredible multiplying bacteria If we wanted

02:50

to see something multiplied this fast we watched that new 00:02:53.24 --> [endTime] show on tlc thirty seven isn't enough

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