Originally Posted by

**paullovesjo** I got this from a maths guru. Unfortunately, he cant fathom how I dont understand it.

Does anyone know how I would enter this into a google calculator and where i would enter say $32,000 into the equation so that I get an answer to the equation?

Alright, if you solve the system of equations I mentioned earlier (either by hand or by using a calculator, say TI83 or TI84), you get the following numbers (there may be rounding error for the numbers listed below):

a_0 = 0.017857

a_1 = -0.01286

a_2 = -0.0045

a_3 = 0.003008

a_4 = -0.00201

a_5 = 0.0015

a_6 = -0.0006

a_7 = -0.001

a_8 = -0.0008

a_9 = -0.0006

Therefore the formula for the function is (denoting square root by sqrt)

f(x) = 0.017857*sqrt((x-0)^2) -0.01286*sqrt((x-700)^2) -0.0045*sqrt((x-1000)^2) +0.003008*sqrt((x-2000)^2) -0.00201*sqrt((x-5000)^2) +0.0015*sqrt((x-10000)^2) -0.0006*sqrt((x-25000)^2) -0.001*sqrt((x-50000)^2) -0.0008*sqrt((x-75000)^2) -0.0006*sqrt((x-100000)^2) + b.

To determine b, substitute 0 for x, since f(0) = 4.95, you get b = 192.475.

In conclusion the sought for formula is

f(x) = 0.017857*sqrt((x-0)^2) -0.01286*sqrt((x-700)^2) -0.0045*sqrt((x-1000)^2) +0.003008*sqrt((x-2000)^2) -0.00201*sqrt((x-5000)^2) +0.0015*sqrt((x-10000)^2) -0.0006*sqrt((x-25000)^2) -0.001*sqrt((x-50000)^2) -0.0008*sqrt((x-75000)^2) -0.0006*sqrt((x-100000)^2) + 192.475.

I have checked the formula in Excel, it works well, since the rounding error is negligible.

To avoid rounding error, you could obtain those a_i by the following formulas, which I have solved for you

a_0 = m_1/2,

a_1 = (m_2-m_1)/2

a_2 = (m_3-m_2)/2

a_3 = (m_4-m_3)/2

a_4 = (m_5-m_4)/2

a_5 = (m_6-m_5)/2

a_6 = (m_7-m_6)/2

a_7 = (m_8-m_7)/2

a_8 = (m_9-m_8)/2

a_9 = -m_9/2,

where m_i is the slope of the line joining (x_(i-1), y_(i-1)) to (x_i, y_i) for i = 1, 2, ..., 9. (For example, (x_0, y_0) = (0, 4.95), (x_1, y_1) = (700, 29.95), hence m_1 = (29.95 - 4.95)/(700 - 0), etc.)