- #1
ProPM
- 66
- 0
Find the values of a and k if the graph with equation f(x) = ae-kx passes through the points (1, e) and (-1,2e)
So, from the information above I managed to derive two equations to solve simultaneously:
ae-k = e
aek = 2e
I am pretty sure those are correct, but I am not 100%. I just think I am having more of a problem solving them!
Here is what I tried:
I tried dividing the second equation by the first:
therefore: ek / e-k = e2k
2e / e = 2, hence:
e2k = 2
To solve for k I did:
(ek)2 = 2 and I let ek = y, hence
y = √2
ek = √2
k log e = 1/2 log 2
k = 1/2 log 2 / log e
I hope my maths is not very confusing, although I do recognized there must be other shorter paths...
Thanks
So, from the information above I managed to derive two equations to solve simultaneously:
ae-k = e
aek = 2e
I am pretty sure those are correct, but I am not 100%. I just think I am having more of a problem solving them!
Here is what I tried:
I tried dividing the second equation by the first:
therefore: ek / e-k = e2k
2e / e = 2, hence:
e2k = 2
To solve for k I did:
(ek)2 = 2 and I let ek = y, hence
y = √2
ek = √2
k log e = 1/2 log 2
k = 1/2 log 2 / log e
I hope my maths is not very confusing, although I do recognized there must be other shorter paths...
Thanks