At the beginning of the year 2000 geologists discovered a rock whose weight was estimated to be one megaton. Each year,due to erosion, the mass of the rock decr

Question

Please help!!!!!!!!!!!!!!

Answer 1

This can be molded by exponential decay which would look like W(t) = W(0) (1/2)^t where W(0) is the initial weight and 1/2 is the rate of decay for the first rock.

If you write two equations, one for each rock and set them equal to each other you would be solving for when their weights are equal. We can adjust the time by assuming t >= 10 and putting t - 10 for the second rock so t still represents the time since 2000.

(1/2)^t = (1/4)^t-10

We can then rewrite the right hand side as the square of (1/2) to have the same base.

(1/2)^t = (1/2)^2t-20

Then we can take the log of both sides and solve for t,

t = 2t - 20

t = 20

Therefor in the year 2020 they shall have the same weight. This can be verified by plugging 20 back into the original equations.