Analysis of Potassium-40 / Argon-40 determines that 37.5% of the Potassium-40 remains and 62.5% has decayed to Argon-40. What is the age of the rock? A. 1.3 billion years B. 0.65 billion years C. 1.95 billion years D. 0.163 billion years

Option C is correct.

t = 1.95 billion years.

Explanation:

Radioactive decay follows a first order reaction kinetics.

On solving the dynamic equation (the differential equation), this is obtained

C(t) = C₀ e⁻ᵏᵗ

C(t) = amount of radioactive material remaining after time t = 37.5%

C₀ = Initial amount of radioactive material = 100%

t = time that has passed = ?

k = decay constant.

For a first order reaction, the decay constant is related to the half life through the relation

k = (In 2)/T

T = half life = 1.38 billion years

k = (In 2)/1.38

k = 0.5023 per billion years.

C(t) = C₀ e⁻ᵏᵗ

0.375 = e⁻ᵏᵗ

e⁻ᵏᵗ = 0.375

In e⁻ᵏᵗ = In 0.375 = -0.981

-kt = -0.981

t = (0.981/0.5023) = 1.95 billion years.

Hope this Helps!!!

the answer is:  

line graphs show patterns in data with variables that change over time; whereas, circle graphs show data as parts out of a whole (such as out of 100%).

every chemical equation adheres to the law of conservation of mass, which states that matter cannot be created or destroyed. therefore, there must be the same number of atoms of each element on each side of a chemical equation.