Answer:
200 million years
Explanation:
The equation that describes the decay of a radioactive isotope is
[tex]N(t)=N_0 (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
where
[tex]N(t)[/tex] is the amount of radioactive isotope left at time t
[tex]N_0[/tex] is the initial amount of isotope
[tex]t_{1/2}[/tex] is the half-life of the sample
In this problem, the ratio between unstable isotope and daughter isotope is 1:15; this means that
[tex]\frac{N(t)}{N_0}=\frac{1}{16}[/tex]
Because the "total proportion" of original sample was 1+15=16.
Also we know that the half-life is
[tex]t_{1/2}=50\cdot 10^6 y[/tex]
So we can re-arrange the equation to find t, the age of the rock:
[tex]t=t_{1/2} log_{0.5}(\frac{N}{N_0})=(50\cdot 10^6)log_{0.5}(\frac{1}{16})=200\cdot 10^6 y[/tex]
So, 200 million years.
