Expert: Sherman D. - 12/26/2008

Question
i want to solve equation y=6.11*Exp((a*x)/(x+b)), and want to know what is the value of a and b. how can we solve it.
Please give me some hint.

Answer
if by this you mean

y = 6.11 * 10^(ax/(x + b))

y/(6.11) = 10^(ax/(x + b))

ln(y/6.11) = (ax/(x + b))ln(10)
ln(y/6.11)/ln(10) = ax/(x + b)
(ln(y/6.11)/ln(10))x + (ln(y/6.11)/ln(10))b = ax

(ln(y/6.11)/ln(10))b = ax - (ln(y/6.11)/ln(10))x
b = (ax - (ln(y/6.11)/ln(10))x)/(ln(y/6.11)/ln(10))
or
b = (a - (ln(y/6.11)/ln(10))/(ln(y/6.11)/ln(10))))x
or
b = (a/(ln(y/6.11)/ln(10))) - 1)x
or
b = (ln(10)/ln(y/6.11))ax - x

using that

b = (ln(10)/ln(y/6.11))ax - x
b + x = (ln(10)/ln(y/6.11))ax
(b/x) + 1 = (ln(10)/ln(y/6.11))a
a = ((b/x) + 1)/(ln(10)/ln(y/6.11))
or
a = ((b*ln(y/6.11))/(x*ln(10)) + (ln(y/6.11)/ln(10))
or
a = (ln(y/6.11)/ln(10))((b/x) + 1)

however if you meant y = 6.11e^((ax)/(x + b)), then

y/6.11 = e^((ax)/(x + b))
ln(y/6.11) = (ax)/(x + b)
xln(y/6.11) + bln(y/6.11) = ax
a = ln(y/6.11) + (b/x)ln(y/6.11)

using that

xln(y/6.11) + bln(y/6.11) = ax
bln(y/6.11) = ax - xln(y/6.11)
b = (ax/ln(y/6.11)) - x
or
b = ((a/ln(y/6.11)) - 1)x

without any values for y or x, thats all i can give you.

the Hint to solving for a and b is inverse of operations.

however if you meant

y = 6.11^((ax)/(x + b))
ln(y) = ((ax)/(x + b))ln(6.11)
ln(y)/ln(6.11) = (ax)/(x + b)
(ln(y)/ln(6.11))x + (ln(y)/ln(6.11))b = ax
a = (ln(y)/ln(6.11)) + (ln(y)/ln(6.11))b
or
a = (ln(y)/ln(6.11))(1 + b)

using that

a/(ln(y)/ln(6.11)) = 1 + b
(ln(6.11)/ln(y))a = 1 + b
b = (ln(6.11)/ln(y))a - 1

sorry i didn't know for sure which one you meant so i did them all.