# SAT Math: Which Equation Models a Company's Exponential Growth?

The number of employees in a rapidly growing business increases by a factor of four every three years. In the beginning, the business had 5 employees. Which of the following equations accurately models the number of employees after t years?

Passport to Advanced Math | Quadratic and exponential functions (word problems) |

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SAT | SAT Math |

SAT Math | Algebra and Functions Passport to Advanced Math |

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### Transcript

the following equations accurately models the number of employees after

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

they got four times five two done five times for

so we got to think through this little bit carefully

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

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

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

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

really Well some people might say this company just has

lots and lots of luck but we can make an

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

revolves around search here That was a better hit for

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

growth will be helpful here in this equation A is

the initial amount b is the growth factor per unit

time that see years t and sees how much time

has passed or how many years has passed So if

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

could be a hard hard question to answer So f

c equals a times quantity b to the sea on

ly two answers have five in the right place Like

where a is that a c and d right there

The hard part is seeing what c should be Well

it takes three years for the number of employees to

grow four times larger than it was before so at

t equals zero We should have the initial amount five

employees then at t equals three We should have five

times four twenty employees and then five times the quantity

for square and that eighty like five times sixteen employees

at equal six So using the fraction t over three

for sea giving us fft equals five times quantity for

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