Answer:
a. about 18 hrs
a. about 50 times larger
Explanation:
"Gold-192 is a radioactive isotope with a half-life of 4.95 hours. How long would it take for a 25 gram sample of Gold-192 to decay until only 2 grams remain?
The amount A left after time t is:
A = P (½)^(t / T)
where P is the initial amount and T is the half life.
Given A = 2, P = 25, and T = 4.95:
2 = 25 (½)^(t / 4.95)
0.08 = ½^(t / 4.95)
log(0.08) = (t / 4.95) log(0.5)
log(0.08) / log(0.5) = t / 4.95
t = 4.95 log(0.08) / log(0.5)
t ≈ 18
"In May 2015, an earthquake originated in Galesburg, MI had a magnitude of 4.2 on the Richter scale. In September 2012, a much smaller earthquake originating in Stony Point, MI had a magnitude of 2.5. The magnitude of an earthquake is given by the formula m = log(I / I₀), where I is the intensity of the earthquake and I₀ is a small reference intensity, how many times larger was the intensity of the Galesburg earthquake compared to the Stony Point earthquake?"
For the Galesburg earthquake:
4.2 = log(I₁ / I₀)
10^4.2 = I₁ / I₀
I₁ = I₀ × 10^4.2
For the Stony Point earthquake:
2.5 = log(I₂ / I₀)
10^2.5 = I₂ / I₀
I₂ = I₀ × 10^2.5
Divide the first equation by the second:
I₁ / I₂ = 10^4.2 / 10^2.5
I₁ / I₂ = 10^(4.2−2.5)
I₁ / I₂ = 10^1.7
I₁ / I₂ ≈ 50