Carbon-14: A = A₀e^kt

First, establish the decay formula for carbon-14 by finding k, the decay constant:
1/2 = 1• e^k•5730
ln(1/2) = 5730k
k = -0.000120968094

A = A₀e^{-0.000120968094t}

Now, utilize this formula to deal with 35% of carbon remaining in the mummy:
0.35 = 1• e^{-0.000120968094t}
ln(0.35) = -0.000120968094t
t = 8678.504305 years

The mummy died approximately 8,678.5 years ago.