Main content

### Course: Get ready for Algebra 2 > Unit 4

Lesson 4: Exponential expressions- Exponential expressions word problems (numerical)
- Exponential expressions word problems (numerical)
- Initial value & common ratio of exponential functions
- Exponential expressions word problems (algebraic)
- Exponential expressions word problems (algebraic)
- Interpreting exponential expression word problem
- Interpret exponential expressions word problems

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Exponential expressions word problems (algebraic)

Given a real-world context that involves repeated multiplication, we model it with an exponential function.

## Want to join the conversation?

- at1:20in the video, how do you figure you can add 1 to .3?(2 votes)
- When something increases by 30%, then you have the original amount, which is 100% + 30%

Change those into decimals and you get 1 + 0.3 = 1.3(25 votes)

- you could've just said 170(1.3)^t

so you really confused me with all that(12 votes) - Can someone please explain the factoring part? Why does it result in 1? Thank you!(4 votes)
- That's the distributive property in reverse, Sal explains it here: https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-polynomials-1-common-factors/v/factoring-linear-binomials

Basically, the two terms, (170) and (170*0.3), (you know they're 2 different terms because they're separated by the plus sign) have 170 as a common factor (because both are divisible by it).

The 1 comes from the fact that the common factor is 170 itself, and 170/170 = 1(6 votes)

- what if the percent is 0(2 votes)
- If the percentage is 0, then there's no increase in the population, so basically there's no need to calculate anything. ;)(9 votes)

- I have a question:

When can we know if our growth rate should be added by 1 or not? For example in the video, Sal added 100% to the increasing growth rate of 30%. Does this always happen in every word problem example?

Sorry if my question is hard to understand, but I'm hoping for someone to answer my question soon. I'm open to answering anyone that needs more clarification for my question! Thx :)(4 votes)- If the problem gives you the percent increase, then you start with the original amount (100%) and add the increase (30%) = 130%

If the problem gives you a percent decrease, then you start with the original amount (100%) and subtract the decrease (30%) = 70%

Hope this helps.(3 votes)

- why aren't you using any of the formulas? it will make it a lot easier for us to understand.(2 votes)
- Hi, Hana B!

Formulas are a handy thing to use, but Sal is trying to explan the principals behind the formula. In my opinion, knowing the mechanics is much more important than just memorizing the formula.

Hope that helped!(7 votes)

- he wrote 170(1+0.3) where the 1 come from?(2 votes)
- As stated in other responses to nearly the same question...

If something grows by 30%, you have the original amount (100%) + the new amount (30%).

If you change these into decimals you get: 100% = 1 and 30% = 0.3

This is where the 1+0.3 comes from.

Hope this helps.

FYI... get in the habit of reading the other questions and answers. They may answer your question and/or give you new insights into the problem.(7 votes)

- what if I have a question that says "there are 50 people in a party and the number of people that know about it increases by 1.5%, how do I do that??

like: if you multiply the percent 30% is 1.3 and 75% is 1.75

so how can 1.5% be like the others??(3 votes)- Hi, you would have to provide more information for us to help you. Like what's the initial value?(2 votes)

- When exponential expressions were first introduced in Khan Academy, I was able to write them like this:

170(1 + 0.3)^t

But now I'm told to write them like this:

170(1.3)^t

And the former version is marked wrong. Why? Is it just to simplify the expression because I've learned the concept?

Edit: Turns out the first version isn't marked wrong, but I'm still wondering why the second is encouraged.(3 votes)- When I see this on tests at school, the second is almost always the ABCD option, I guess the reason is what you say, it is the simplified version.(2 votes)

- It really helped(3 votes)

## Video transcript

- [Instructor] There are
170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives
the deer population P of t on the reservation t years from now. All right, let's think about this. And like always, pause this video, and see if you can work
it out on your own. Well, let's think about what P of zero is. P of zero, this is going to be the initial population of deer, the population at time zero. Well, we know that, that's
going to be the 170 deer that we start on the reservation. Now, let's think about what P of one is. What's going to be the
population after one year? Well, it's going to be our
original population, 170, but then it increases at
a rate of 30% per year. So it's going to be 170
plus another 30% of 170. So I could write that as 30% times 170. Or I could write this as 170 plus 0.3 times 170. 30% as a decimal is the same
thing as 30/100 or 3/10. Or I could write this as, if I factor out 170, I would get 170 times one plus 0.3, which is the same thing as 170 times 1.03. And this is a really good
thing to take a hard look at 'cause you'll see it a lot when we're growing by a certain rate, when we're dealing with what turns out to be
exponential functions. If we are growing, well, I almost made a
mistake there, it's 1.3. So here you go, 1.3. One plus 0.3 is 1.3. So once again, take a hard
look at this right over here because it's going to be something that you see a lot with
exponential functions. When you grow by 30%, that means you keep your
100% that you had before, and then you add another 30%. And so you would multiply your
original quantity by 130%, and 130% is the same thing as 1.3. So if you are growing by 30%, you are growing by 3/10, you would multiply your
initial quantity by 1.3. So let's use that idea to keep going. So what is the population after two years? Well, you would start that second year with the population at
the end of one year. So it's going to be that 170 times 1.3. And then, over that year,
you're going to grow by another 30%. So if you're gonna grow by another 30%, that's equivalent to
multiplying by 1.3 again. Or you could say that this
is equal to 170 times 1.3 to the second power. And so I think you see
where this is going. If we wanted to write a general P of t, so if we just want to
write a general P of t, it's going to be whatever
we started with, 170, and we're going to multiply that by 1.3 however many times, however
many years have gone by. So to the t power because, for every year, we grow by 30%, which is equivalent mathematically
to multiplying by 1.3. So after 100 years, it would be 170 times
1.3 to the 100th power.