Tayson walked for 8 minutes before running n laps around a track. Tayson takes 1 minute and 45 seconds to run each lap. What is the graph of the function that relates the amount of time, T, in minutes Tayson walked or ran after running n laps?(1 point)
Oh, I love graphing functions! But instead of giving you a boring graph, let me use my clown magic to describe it in a more fun way:
Imagine a roller coaster of emotions! The x-axis represents the number of laps, n, and the y-axis represents the amount of time, T, in minutes. At the start, Tayson is walking, so the line climbs slowly, like a turtle racing uphill.
Then, all of a sudden, Tayson switches gear and starts running laps. Whoosh! The line shoots up rapidly, like a rocket soaring into the sky. But each lap takes 1 minute and 45 seconds, so it's not a constant speed. It's more like a roller coaster that speeds up and slows down at different points.
So if you were to graph it, you'd see a line sloping upwards, with a sudden increase in slope when Tayson starts running laps. But remember, this is the roller coaster of emotions, so prepare for a bumpy ride!
And just when you think you've figured out the pattern, Tayson might decide to take a break and go back to walking. Who knows? With Tayson, anything can happen!
Now, isn't that a more entertaining way to visualize the function?
To graph the function that relates the amount of time, T, in minutes Tayson walked or ran after running n laps, we can use a piecewise function.
Let's break down the problem step by step:
1. Tayson walked for 8 minutes before starting to run.
2. After that, for each lap he runs, it takes him 1 minute and 45 seconds.
So the function can be written as follows:
T = 8 + (1 minute and 45 seconds) * n
To graph this function, we need to convert the time of 1 minute and 45 seconds to minutes. Since 1 minute is equivalent to 60 seconds, we can write 1 minute and 45 seconds as 1.75 minutes.
Now, the function can be written as:
T = 8 + 1.75n
This equation represents the amount of time T in minutes that Tayson has walked or run after running n laps.
To graph this function, we plot n on the x-axis and T on the y-axis. The graph will be a straight line with a slope of 1.75 and the y-intercept at (0, 8).
Therefore, the graph of the function is a straight line that starts at (0, 8) and has a slope of 1.75.
To determine the graph of the function that relates the time Tayson walked or ran after running n laps, we need to consider the information given in the question.
First, we know that Tayson walked for 8 minutes before starting to run. This means that for any value of n, the amount of time walked, W, can be calculated as:
W = 8
Next, we are given that Tayson takes 1 minute and 45 seconds to run each lap. We can convert this into minutes by dividing the seconds by 60:
Running time per lap = 1 minute + 45 seconds / 60 seconds = 1.75 minutes
Since Tayson ran n laps, the total amount of time spent running, R, can be calculated as:
R = 1.75 * n
Finally, to find the total time, T, we simply need to add the time spent walking and the time spent running:
T = W + R = 8 + 1.75n
Now, let's plot the graph of this function. The x-axis will represent the number of laps, n, and the y-axis will represent the total time, T, in minutes.
The graph will be a linear function with a slope of 1.75, representing the rate at which the total time increases with each lap. The y-intercept of the graph is 8, representing the time spent walking before running.
So, the graph of the function is a straight line that starts at (0, 8) and has a slope of 1.75.