Daniel is playing his favorite video game and noticed that the points he earned every minutes follow a linear pattern. Here is a table showing his total points for the first several minutes of play.
Minutes:x. Points: f(x)
0. 1550
1. 1900
2. 2250
3. 2600
4. 2950
1. Write a function that represents this scenario.
My answer is f(x) =1550x
2. After 10 minutes, how many points will he have?
My answer is 15500
3. If Daniel has 12,050 points, how many minutes has he been playing?
My answer is 7 minutes.
Oh my, it says linear which means of form
f(x) = m x + b
You assumed that it wnnt through zero but it goes through
(0,1550)
so in fact it is of form
f(x) = m x + 1550
where m is the slope
slope = (2950-1550)/4 = 350
so I get
f(x) = 350 x + 1550
Thanks Damon.
You are welcome.
1. The given scenario shows a linear relationship between the number of minutes played (x) and the total points earned (f(x)). To write a function that represents this relationship, we can use the formula for a linear equation, which is f(x) = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Using the given data, we can calculate the slope as follows:
m = (1900 - 1550) / (1 - 0) = 350 / 1 = 350
Now, to find the y-intercept (b), we can substitute the values of x and f(x) into the linear equation:
1550 = (350)(0) + b
Simplifying the equation, we get:
b = 1550
The function that represents the scenario is f(x) = 350x + 1550.
2. To find the number of points Daniel will have after 10 minutes, we can substitute x = 10 into the function:
f(10) = 350(10) + 1550
f(10) = 3500 + 1550
f(10) = 5050
After 10 minutes, Daniel will have 5,050 points.
3. To find the number of minutes Daniel has been playing if he has 12,050 points, we need to solve the function for x:
12,050 = 350x + 1550
Subtracting 1550 from both sides of the equation:
12,050 - 1550 = 350x
10,500 = 350x
Dividing both sides by 350:
x = 30
Therefore, if Daniel has 12,050 points, he has been playing for 30 minutes.