ShmoopTube

00:03

Okay Shh Mash bumpers Another word problem coming at us

00:07

The number of employees and a rapidly growing business increases

00:10

by a factor of four every three years That is

00:14

they go from like one hundred four hundred three years

00:17

In the beginning the business had five employees which of

00:20

the following equations accurately models the number of employees after

00:24

t years All right so what we're looking at these

00:31

they got four times five two done five times for

00:34

so we got to think through this little bit carefully

00:35

for a company to grow this fast they'd have to

00:38

be super successful smart and good looking We're not saying

00:42

this mystery company is from up at all We're just

00:44

saying that we're super successful smart and good looking Not

00:48

really Well some people might say this company just has

00:51

lots and lots of luck but we can make an

00:53

equation to predict their luck It's an algorithmic one that

00:57

revolves around search here That was a better hit for

01:00

the company we're talking about Well the equation for exponential

01:02

growth will be helpful here in this equation A is

01:05

the initial amount b is the growth factor per unit

01:08

time that see years t and sees how much time

01:12

has passed or how many years has passed So if

01:14

you didn't get this equation well a good luck it's

01:17

could be a hard hard question to answer So f

01:20

c equals a times quantity b to the sea on

01:23

ly two answers have five in the right place Like

01:26

where a is that a c and d right there

01:28

The hard part is seeing what c should be Well

01:31

it takes three years for the number of employees to

01:33

grow four times larger than it was before so at

01:37

t equals zero We should have the initial amount five

01:41

employees then at t equals three We should have five

01:45

times four twenty employees and then five times the quantity

01:50

for square and that eighty like five times sixteen employees

01:54

at equal six So using the fraction t over three

01:57

for sea giving us fft equals five times quantity for

02:01

two the third there So the answer is c and 00:02:05.557 --> [endTime] wow this pretty hard problem that we're done

Full Transcript