Question
Raimy surveyed 10 people, asking them the number of miles they drove last week
and the number of gallons of gas they used. The following table shows his results:
Number of
Miles Driven
Number of
Gallons of Gas
Used
80 3
140 5
140 4
150 4
180 5
250 7
260 8
300 8
350 12
450 15
Can this data set be best modeled with a linear function, a quadratic function, or an exponential function? Explain. already done.
Raimy asked 10 people how far they drove and how much gas they used. When we look at the numbers, it seems like the more miles people drove, the more gas they needed, but not in a simple straight line. Instead, it looks like the amount of gas goes up faster as the miles increase, which suggests it's not a straight line (linear) or a curve that opens up or down (quadratic). It looks more like an exponential function because the gas usage gets bigger quickly with the longer miles.
Use technology to create an appropriate regression model. Explain the steps you took and your result.
make it simple in a small paragraph and like a kid wrote it.
and the number of gallons of gas they used. The following table shows his results:
Number of
Miles Driven
Number of
Gallons of Gas
Used
80 3
140 5
140 4
150 4
180 5
250 7
260 8
300 8
350 12
450 15
Can this data set be best modeled with a linear function, a quadratic function, or an exponential function? Explain. already done.
Raimy asked 10 people how far they drove and how much gas they used. When we look at the numbers, it seems like the more miles people drove, the more gas they needed, but not in a simple straight line. Instead, it looks like the amount of gas goes up faster as the miles increase, which suggests it's not a straight line (linear) or a curve that opens up or down (quadratic). It looks more like an exponential function because the gas usage gets bigger quickly with the longer miles.
Use technology to create an appropriate regression model. Explain the steps you took and your result.
make it simple in a small paragraph and like a kid wrote it.
Answers
GPT-4o mini
I used a computer program to find out what kind of math equation fits Raimy's data best. First, I put all the miles and gas numbers into the program. Then, I asked it to try different kinds of equations: a straight line, a curve that goes up and down, and a curve that goes up really quickly. The program showed that the curve that goes up quickly (like an exponential function) matched the data the best. In the end, I found an equation that helps predict how much gas people will use based on how many miles they drove!