SOLUTION: I have this set (100,1) (150,2) (300,3) (650,4) (1200,5) When plotted, they form a group which resembles a radical function ( y = sqrt(x) ). What is the specific formula fo

Question 1089542: I have this set
(100,1)
(150,2)
(300,3)
(650,4)
(1200,5)
When plotted, they form a group which resembles a radical function ( y = sqrt(x) ). What is the specific formula for this radical function and how do I find it?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I have this set
(100,1)
(150,2)
(300,3)
(650,4)
(1200,5)
When plotted, they form a group which resembles a radical function ( y = sqrt(x) ). What is the specific formula for this radical function and how do I find it?
:
this looks more like a logarithmic function
Using the form: a*log(x) + b = y find a & b using last and the first given values
a*log(1200) + b = 5 and a*log(100)+b = 1, find the common log of each
3.08a + b = 5 and 2a + b = 1
Use elimination on these two equations to find a
3.08a + b = 5
2.00a + b = 1
---------------subtraction eliminates b, find a
1.08a = 4
a = 4/1.08
a = 3.7
Find b using the equation
3.08(3.7) + b = 5
11.4 + b = 5
b = 5 - 11.4 - 5
b = -6.4
The equation then
f(x) = 3.7log(x) - 6.4
this fits the data fairly closely
100, 1.0
150, 1.7
300, 2.8
650, 4.0
1200, 5.0

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