Question 1187434
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It's hard to know how to respond, since we have no idea of your level of mathematical knowledge....<br>
Following is one way to find the equation giving the number of meters as a function of the number of minutes.<br>
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.).<pre>
1   3   6  10  distances in meters after 1, 2, 3, and 4 minutes
  2   3   4    "first differences"
    1   1      "second differences"</pre>
The constant second differences tell us the equation is quadratic -- of the form<br>
{{{f(x)=ax^2+bx+c}}}<br>
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.<br>
f(1): a+b+c=1  [1]
f(2): 4a+2b+c=3  [2]
f(3): 9a+3b+c=6  [3]<br>
[3]-[2]: 5a+b=3  [4]
[2]-[1]: 3a+b=2  [5]<br>
[4]-[5]: 2a=1; a=1/2  [6]<br>
Substitute [6] in [5]: 3/2+b=2; b=1/2  [7]<br>
Substitute [6] and [7] in [1]: 1/2+1/2+c=1; c=0<br>
The coefficients are
a=1/2
b=1/2
c=0<br>
ANSWER: The equation is<br>
{{{f(x) = (1/2)x^2+(1/2)(x)}}}<br>
or, in other possible forms,<br>
{{{f(x) = (1/2)(x^2+x)}}}
{{{f(x) = (1/2)(x)(x+1)}}}<br>