stuck on a diff eq problem

[recipro]

Let 10pm be time X. Then 11pm is time X+1...
31 = 22e^(kx) + 15 ...
16/22 = e^(kx) ...
ln (8/11) = kx
k = ln (8/11) / x

Now, plug in x+1...
29 = 22e^(kx+k) + 15 ...
14/22 = e^(kx+k)
ln (7/11) = k (x+1)
ln (7/11) = ln (8/11) * (1 + 1/x)

I don't feel like doing the rest, but solve for x obv.