Ineed with the gold-192 and magnitude of the earthquake.

a. about 18 hrs

a. about 50 times larger

Step-by-step 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

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.

55? i think maybe

step-by-step explanation: