A sample of polomium-210 has a mass of 300 milligrams. After 1 year, 49 milligra

Question

A sample of polomium-210 has a mass of 300 milligrams. After 1 year, 49 milligrams remain. a.) Find a function A(t)=A0e^-kt that models the amount of the sample remaining at time t. Round the value of k to four decimals. b.) How long will it take for the sample to decay to a mass of 200 milligrams? Round answer to two decimal places. Please help if can and show work. Thank you!

Explanation / Answer

Using the form, A(t)=A0e^-kt and knowing that at t =0, we have 300 milligrams, we can say A(t)=A0e^(0) ==> A0 = 300. Now we have A(t)=300e^-kt. Putting in t = 1, we have 49 = 300e^-k. Solving for k, we get k = -ln(49/300) or ln(300/49) which is about 1.812. SO we finally get A(t)=300e^-1.812t. For part B, we simply plug in 200 for A(t) and we get t = .22 years

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.