Question 1187434: a toy car was made to run the length of a room. Suppose its speed increase so that it ran 1 meter the first minute, 2 meters in the second minute, 3 meters in the third minute, and so on. The speed is increasing about 1 meter each minute. The relation between the distance of the toy car from the starting point and the number of minutes it has run is shown below
time (X) 0 1 2 3 4
distance (y) 0 1 3 6 10
1. Determine the equation with the given table of values
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
It's hard to know how to respond, since we have no idea of your level of mathematical knowledge....
Following is one way to find the equation giving the number of meters as a function of the number of minutes.
If you don't understand this method, re-post the question, indicating what level of math you have studied (algebra I, algebra II, pre-calculus, etc.).
1 3 6 10 distances in meters after 1, 2, 3, and 4 minutes
2 3 4 "first differences"
1 1 "second differences"
The constant second differences tell us the equation is quadratic -- of the form
Use f(1)=1, f(2)=3, and f(3)=6 to form three equations that can be solved to find the coefficients a, b, and c and thus find the equation.
f(1): a+b+c=1 [1]
f(2): 4a+2b+c=3 [2]
f(3): 9a+3b+c=6 [3]
[3]-[2]: 5a+b=3 [4]
[2]-[1]: 3a+b=2 [5]
[4]-[5]: 2a=1; a=1/2 [6]
Substitute [6] in [5]: 3/2+b=2; b=1/2 [7]
Substitute [6] and [7] in [1]: 1/2+1/2+c=1; c=0
The coefficients are
a=1/2
b=1/2
c=0
ANSWER: The equation is
or, in other possible forms,
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