SOLUTION: I want to solve the equation:
0.95 = exp(-a)+a*exp(-a) = exp(-a)*(1+a)
The first step I guess would be to take the natural log:
ln(0.95) = ln(1+a)-a
Please help!
Matt
Question 10298: I want to solve the equation:
0.95 = exp(-a)+a*exp(-a) = exp(-a)*(1+a)
The first step I guess would be to take the natural log:
ln(0.95) = ln(1+a)-a
Please help!
Matt Answer by mathmaven53(29) (Show Source):
You can put this solution on YOUR website! You can't solve for a algebaicly
We try a numerical approach
We have exp(-a)(1+a) = .95
Then 1 + a = .95 exp(a)
Plot the functions f(a) = 1+a and g(a) = .95 exp(a)
See where they intersect and estimate an approximate value of a
Call this value of a
a_0
Try iterating values in the recursion relation
a_(n+1) = .95 exp(a_n) - 1
Note: a_0 is read a sub zero, a_(n+1) is read a sub n plus one
When you get values of this sequence that don't differ by much then quit
the iterations. Then you have an approximate value of a
(