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### Course: Algebra 1 > Unit 12

Lesson 2: 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

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# Interpreting exponential expression word problem

Given an exponential function that models a real-world context, we interpret it to see what each part of the function represents in the real world.

## Want to join the conversation?

- how does one differentiate between initial value and later value?(8 votes)
- The initial value is the starting value. The number of something before you multiply or divide it by anything. Later value is the initial value after you multiply it by what the equation tells you to. In the video at2:17, Sal shows the initial value at 5. You can tell the initial value from everything else because it is almost always the first number on the business end of the = sign.

L(t) = 5(2)^t

the first number is 5. Nothing else is multiplied by anything else, (not an exponent) so it is the initial value.

Hope this helps.(7 votes)

- What is p(t) don't understand(4 votes)
- p(t) is what the value p is when t is a certain value. For example, if t=2 and the function is p(t)=5+t, then you would first plug in the values for t --> p(2)=5+2, which equals 7. So, p(2) equals 7. If it helps you can think of it like an output, or y value.(10 votes)

- Can growth rate be negative? So like, decreasing rate?(3 votes)
- Yeah, it would just have to have a number there less then 1.(2 votes)

- What is the difference between the common ratio of the exponential function and the growth rate?(3 votes)
- They are closely related to each other. If you have a growth rate of 5%, Then the common ratio will end up being 1+.05=1.05. If you double every unit rate, then the common ratio would be 2, but the growth rate would be 100% (100%=1 and 1+1=2). Tripled would give common ratio of 3, but a growth rate of 200%(4 votes)

- What's the answer to this question?

when you fold a piece of paper in half, the thickness of the folded piece is twice the thickness of the original piece. a piece of copy paper is about 0.1 mm thick.

a. how thick is the copy paper folded 7 times?

b. suppose you could fold a piece of copy paper 12 times. how thick would it be in centimeters?(3 votes)- First off, I hope that this isn't a test question.

Second, you would write the equation as P(f)=0.1(2)^f

Let p equal paper

let f equal number of times folded

For the second part, you would plug 12 into your equation in the place of (f), and then after you solve, divide by ten to get the answer in centimetres.(3 votes)

- The initial value is the starting value. The number of something before you multiply or divide it by anything. Later value is the initial value after you multiply it by what the equation tells you to. In the video at2:18?(3 votes)
- This is a every relevant problem for Praxis takers. However Praxis may offer the base as 3.05 and the exponent as 1.98. Take should round these numbers, then test simple values for t (time)(3 votes)
- In this problem we start from 0th week. Sometimes we start from week 1/count 1. How to interpret from the question on when to start the count from 0 and when to start the count from 1(2 votes)
- The initial value describes what you have in week 0.

In other words, week 0 is kind of like a starting value, whereas the common ratio is what you multiply the initial value so that you move on to week 1. You basically have to read the context. Most exponential functions will have both a week 0 and a week 1. The multiplier from week 0 to week 1 is the common ratio and the starting value at week 0 is the initial value.(2 votes)

- I tink I would die before I understand any of this(1 vote)
- I don't know for you, but for me geomentry is ten times harder(1 vote)

- can there be a decreasing rate(1 vote)

## Video transcript

- [Instructor] The expression
five times two to the T gives the number of leaves in a plant as a function of the number
of weeks since it was planted. What does two represent
in this expression? So pause this video and see
if you can figure it out on your own. All right, so let's look at
the expression right over here. We could write it as defining a function. So we could say leaves
as a function of time is equal to five times two to the T power and so we could try this out a little bit. If we say well what is L of zero? That would be T equals zero. That's when we are at zero
weeks after it was planted. So this is right when it was planted. Well that's five times two to the zero, which is just two to the zero's just one. So it's equal to five and so when you see an
exponential expression or an exponential function like this, that is why this number out here is often referred to
as your initial value. Initial. Initial value. And so let's explore
this a little bit more. What is L of one? What happens after one week? Well that's gonna be five
times two to the first power or five times two. So going from when it was
planted to the first week, we are multiplying by two. The number of leaves doubles. Well what happens after two weeks, the number of leaves after two weeks? Well that's gonna be five
times two to the second power. Well that's the number that
you had in the first week times two. So it looks like every
week we are doubling, we are multiplying by two and that's why this
number right over here, which is what the question
is about, the two, this is often referred
to as the common ratio. Common ratio. Because between any two successive weeks, the ratio between say week
two and week one is two. Week two is double week one. Week one is double week zero. So let's see which of these choices actually match up to that. There were initially
two leaves in the plant. Well we know that there weren't
two leaves on the plant. Our initial value was five. So let me cross that one out. The number of leaves is
multiplied by two each week. Well that's exactly
what we just described. So I like that choice. Let's look at the last
one just for good measure. The plant was planted two weeks ago. Well no, they don't tell
us anything about that. This is a general expression for T weeks after it was planted. So they're not saying when
it was actually planted. So we could rule that out and we feel good about that second choice.