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SAT Math: Which Equation Models a Company's Exponential Growth? 3 Views
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Description:
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?
Transcript
- 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
Full Transcript
- 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
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