Exponential Function question

Question

Radon-222 decays at a continuous rate of 17.3% per day. How much will 500 mg of Radon-222 decay to in 10 days?

So__________________ mg of Radon-222 will remain. Round answer to 5 decimal places.

Answer 1

Use the formula Rn_t = Rn₀(1-r)^t where Rn_t is the amount of Radon-222 left after t days, Rn₀ is the amount of Radon-222 you started with, r is the decay rate, and t is the number of days it decays.

 

Rn₁₀ = 500mg(1-.173)¹⁰

Rn₁₀ = 500(.827)¹⁰

Rn₁₀ = 500(.1496425484)

Rn₁₀ = 74.8212742

 

So 74.82127 mg of Radon-222 will remain.