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## Passport to advanced mathematics

Current time:0:00Total duration:3:30

# Quadratic and exponential word problems — Basic example

## Video transcript

- [Instructor] A cable
company with a reputation for poor customer service
is losing subscribers at a rate of approximately 3% per year. The company had two million subscribers at the start of 2014. Assume that the company
continues to lose subscribers at the same rate and that
there are no new subscribers. It's truly a bad situation
for them (chuckles). Which of the following functions, S, models the number of
subscribers, in millions, remaining t years after the start of 2014? So let's just think
about this a little bit. So S of zero, when t equals zero, this is zero years
after the start of 2014. So this would be the number
of subscribers they had at the start of 2014,
which is two million. So S of zero is going to be two. Remember, S is in terms of
millions, they tell us that. So S of zero is two. What is S of one going
to be, when t equals one? Well, one year has gone by, so they're going to lose
3% of their subscribers, and losing 3% is the same
thing as retaining 97%. So it's going to be two times 0.97. Now what happens at t
equals two, after two years? Well, they started with two million. In one year, they were able
to, only to retain 97%. And then another year goes by. They're only gonna retain 97%
of what they had or after, what they had the year
before, so another 97%. So I see, I think you see the trend. You're going to multiply
by 97% as many times or as t times I guess is another
way to think about it. If you say S of three, you started with two million subscribers, after one year you retain 97% of them, after another year you're
gonna retain 97% of this, and after another year, at t equals three, you're gonna retain 97% of that, 97% of that. So in general, S of t, it's going to be what you
started with times 0.97 to the t-th power. However many years have
gone by, you take your, I guess you'd say your
retention rate to that power. And of course, you then multiply that times your initial starting subscribers, and that's how much
you're gonna be left with. And let's see, which of
these choices have that? That is this choice right over here. Now another way you could've done it is you could've tried to
rule out some choices here. This one actually has
the subscribers growing. If you multiply by 1.03 to the t, 1.03 times 1.03 times 1.03, it's going to get larger than one. You're gonna have more than
two million subscribers, so as t increases, so you
could rule that one out. In this one, every year, you're only retaining
70% of your subscribers. You're losing 30%, not 3%, so that one's even worse than
this already bad situation. And then this one, this is a linear, this is kind of a, well, it's, I mean, they're saying
you're multiplying by t. And, you know, one way to
realize that this is gonna break down very fast is t equals zero, this is gonna give us zero. But at t equals zero, you
don't have zero subscribers. At t equals zero, you have
two million subscribers. The other way to think about
it is this one's gonna increase as t increases, while we need
to have a decreasing number of subscribers, so you could
rule that one out as well.