If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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?
• 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 at , 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.
• What is p(t) don't understand
• 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.
• 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?
• 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.
• What is the difference between the common ratio of the exponential function and the growth rate?
• 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%