I'm interested in the equation y = e^(x+a).
2006-11-25 15:46:16 · 6 answers · asked by Bobbi L 1 in Science & Mathematics ➔ Mathematics
If by 'convert' to a linear function you mean approximate by a linear function, then a possible solution is given by the Taylor's expansion of the exponential function.
Consider a point x0, then the linear approximation of y around x0 is given by:
y(x) = e^(x0+a) + e^(x0+a) * (x+a-x0) ,
which is linear in x. Obviously this is only an approximation as the Taylor expansion of the exponential function will involve a very large number of higher order (i.e. quadratic, cubic etc) terms in the right hand side of the equation.
2006-11-25 17:56:41 · answer #1 · answered by Feri 1 · 0⤊ 0⤋
One doesn't. About the best that can be done is to plot the logs of both sides against each other on logarithmic graph paper. That will give you a 'straight line'. But it's *not* a linear function.
Douyg
2006-11-25 15:52:56 · answer #2 · answered by doug_donaghue 7 · 1⤊ 0⤋
Use semi-log graph paper to plot.
2006-11-25 19:47:45 · answer #3 · answered by Jerry M 3 · 0⤊ 0⤋
graph the natural log of both sides
ln(y) vs x+a
2006-11-25 15:48:44 · answer #4 · answered by Erik N 2 · 1⤊ 0⤋
take the ln of both sides to get
ln(y) = x + a
make ln(y) as one of your axis
2006-11-25 15:48:09 · answer #5 · answered by rawfulcopter adfl;kasdjfl;kasdjf 3 · 1⤊ 0⤋
ln(y) -= x+a
2006-11-25 15:48:10 · answer #6 · answered by geek31459 2 · 1⤊ 0⤋