Answer:
4155 years
Step-by-step explanation:
The exponential equation can be solved by using logarithms to transform it to a linear equation.
The problem statement tells you that for some initial amount of C-14 equal to N0, the remaining amount is N = 0.66N0. That means the equation you need to solve is ...
0.66 = e^(-0.0001t) . . . . . . factor of N0 in 0.66N0 and N0·e^() divided out
Taking natural logs, you have ...
ln(0.66) = -0.0001t
t = -ln(0.66)/0.0001 ≈ 4155
The age of the spear head is about 4155 years.
