If 60% of a radioactive element remains radioactive after 200 million years, then what percent remains radioactive after 500 million years?
Once you do that, you realize it is reasonable, as at 200 million years, it has not reached the first half life yet, and at 500 million years, it has, and not quite half is left.
Good work, Lola. Thanks.
m = M e^-kt
m/M = 0.60 = e^-k(200)
ln 0.60 = -200 k
-.511 = -200 k
k = 0.00170/million years
m/M = e^-0.00170(500)
= 0 .427
so
42.7 %
for half life
0.5 = e^-.00170 t
ln .5 = -.0017 t
solve for t in millions of years
To find out what percent of the radioactive element remains after 500 million years, we can use the concept of exponential decay. Given that 60% of the element remains after 200 million years, we can set up the equation:
P(t) = P₀ * (1 - r)ᵗ
Where:
P(t) = percentage of the radioactive element remaining after time t (in this case, 500 million years)
P₀ = initial percentage (60%)
r = decay rate (unknown)
t = time (in this case, 500 million years)
To solve for r, we need to rearrange the equation:
r = 1 - (P(t)/P₀)^(1/t)
Plugging in the given values:
r = 1 - (P(500 million years)/60%)^(1/500)
Let's calculate the value of r.