You can
put this solution on YOUR website! Find an exponential function of the form f(x) = a * e^(b/x) + c that has y-intercept (0,5), a horizontal asymptote y = 3, and whose graph passes through the point (4,10)."
"a horizontal asymptote y = 3" means " when x-->+/- oo, y-->3"
(you are right my can never be 3.]
In this exponential case, if b> 0 and lim f(x) exists as x-->+oo,
then lim f(x)--> a*0 + c= c, so y=c=3.
When b > 0, lim f(x) --> c=3 as x-->-oo.
We claim, c = 3.
Now, f(0) = a*1 + 3 = 5, so a = 2.
Next, use f(4) = 2e^(b/4) + 3 = 10, or e^(b/4) = 7/2.
So b = 4ln(7/2) [stop here, don't make ugly decimals or approx.]
Answer f(x) = 2 e^(4/x * ln(7/2)) +3.
[Note ; e^(4/xln(7/2)) = (7/2)^(4/x)]
Kenny
PS: It is important for me that you posted these two questions in
wrong category. Never happen again!
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