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# Modeling with basic exponential functions word problem

Sal solves a word problem where he models the growth of a speeding ticket fine over time as an exponential function, and then interprets this model. Created by Sal Khan.

## Want to join the conversation?

• whats the diffrences between geometric progression and exponential function as both have a , r
• An exponential function is essentially the continuous version of a geometric progression. It is a function of any real number, not just the positive integers.
• What is the decay rate and decay factor for this situation, or does this problem even have a decay rate or factor?
• This ticket fine example has a common ratio of 1.5. It shouldn't be referred to as a decay factor since it is increasing, but it plays the same role in this exponential function.
• How can we algebraically solve a problem like this: 5(to the x power) = 625
what is the mathematical way to find x ?
• The inverse of exponents is logarithms. You would do log base 5 (5^x) equals log base 5 (625) and get the final answer to be 4.
• is this the same thing as
f(x)= (2)x
• but that's the same thing as the f(x)=(2)x !
• Calculate \$1,224investment after 10 years at 3.5%APR for interest compounded yearly, quarterly, monthly and daily
• how do you solve exponential function if we don't have common ratio
• If you have two points on a graph or two numbers in a table, you can find out what the common ratio is. If you don't have enough information to do that, I doubt that you will be able to solve the function.
(1 vote)
• How did Sal get 1.5?
(1 vote)
• 450/300 = 1.5
675/450 = 1.5
1012.5/675 = 1.5
The common factor to go from one value to the next using mulitplication is 1.5. We use division to find the common factor.
• What's dividing by 1.5 called verbally ? like if we divided by 2 that means we divided into 2 groups, so what about 1.5 ?
(1 vote)
• 1.5 can be written in many different ways but for the purposes of answering your question 1.5 is the same thing as "three-halves".
This is because 1 is the same thing as 2/2 and
0.5 is the same as 1/2
So (1.0 + 0.5) = (2/2 + 1/2) = 3/2
Which is pronounced "three-halves".
• The ticket fine increases at a rate of 50% per month, doesn't it?

P.S.: The function can be interpreted as saying "art" (F(t) = ar^t).
(1 vote)
• Yes, the ticket fine increases at a rate of 50% per month.

P.S. F(t) is the fine so Fine is ar^t and therefore ar^t is fine :D