linear and exponential graphs and x,y intercepts

[Mozam.ali]

I have two lines one linear (y=mx+c) and one exponential (y=c^bx) and
they intercept each other. I believe it is possible to calculate where
the lines intercept. Although I can do this by graphing the data, it
takes time and allows for user error so a calculation would speed
things along greatly.

The problem:

So for the first line using the equation y=mx+c the numbers for the
13kPa line are y=0.0021x+9e-16

And for the exponential line (y=c^bx) which we produce to using the
myograph is y=0.0022^0.0046x (^=Exp)

I know that the two lines intercept at 1613. But no matter what I try
I can't get the equations to simplify and produce a x value.

 

[Bernard Liengme]

I would suggest that y=0.0021x+9e-16 is essentially y=0.0021x (the error in
m is greater then the value of c)
This makes the math trivial
best wishes

 

[Tushar Mehta]

The way to solve this is to set the 2 equations equal to one another and
then solve for x. So, you will get
0.0021x+9e-16 = 0.0022*EXP(0.0046x)

For all practical purposes 9e-16 is zero. So, we get
0.0021x = 0.0022*EXP(0.0046x)

This cannot be solved algebriacally but it can be solved numerically.

Designate a cell, say B2 as the one containing the X value. Then, in C2,
enter the formula =0.0021*B2. In D2, enter the formula
=0.0022*EXP(0.0046*B2). In E2 enter the formula =C2-D2.

Now, use GoalSeek (Tools | Goal Seek...) to set E2 to zero by changing B2.
Though, given the scale of the numbers, I would go with Solver (Tools |
Solver...) Set the target as E2, set the desired value of 0 and click
Solve.

I get two results, both borne out by a chart. The first intersection is
reached if you start with an initial value of 0 in B2. The second by
starting with an initial value of 2000.

And, for the larger result, I don't get 1631 but 1593.

--
Regards,

Tushar Mehta
www.tushar-mehta.com
Excel, PowerPoint, and VBA add-ins, tutorials
Custom MS Office productivity solutions

 

[Mozam.ali]

More help needed.

I do not have solver installed on my PC and the logistics of getting it
put onto every PC at work is going to be impossible. So I can't use
the solver. I do have GoalSeak if thats any help.

Next although the y-value for this equation is near zero that will not
be the case in all the eqautions i deal with. the equations are just
an example.

I want to know at what X-value do the two lines cross.

I would preferably want it as an eqaution because I need to construct
it using XL. Also I have done much in the way of mathematics since uni
(about 7 years ago) so you will have to go slow. I know it's a
terrible excuse, but I need to understand it all.

mc+c=c^bx (^=exp).