A radioactive material decays according to the function , where is the initial amount present and
is the amount present at time (in years). Assume that a scientist has a sample of 500 grams of the radioactive
material.
(a) What is the decay rate of the radioactive material?
(b) Graph the function using a graphing utility.
© How much radioactive material is left after 30 years?
(d) When will only 400 grams of the radioactive material be left?
(e) What is the halt-life of the radioactive material?

Ask by Mathis Frazier. in the United States

Jan 22,2025

Question

A radioactive material decays according to the function , where is the initial amount present and
is the amount present at time (in years). Assume that a scientist has a sample of 500 grams of the radioactive
material.
(a) What is the decay rate of the radioactive material?
(b) Graph the function using a graphing utility.
© How much radioactive material is left after 30 years?
(d) When will only 400 grams of the radioactive material be left?
(e) What is the halt-life of the radioactive material?

Ask by Mathis Frazier. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

Let's analyze each part of the problem step by step.

### **Given:**
- **Decay function:** $$ A(t) = A_{0} e^{-0.0244 t} $$
- **Initial amount ($$ A_{0} $$):** 500 grams
- **Time ($$ t $$):** in years

---

### **(a) What is the decay rate of the radioactive material?**

**Decay Rate Explained:**
The decay rate in the exponential decay function $$ A(t) = A_{0} e^{-kt} $$ is represented by the constant $$ k $$. This rate determines how quickly the material decays over time.

**Given Function:**
$$ A(t) = A_{0} e^{-0.0244 t} $$

Here, the decay constant $$ k $$ is **0.0244**.

**Units:**
Since time $$ t $$ is in years, the decay rate has units of **per year**.

**Final Answer:**
The decay rate of the radioactive material is **0.0244 per year**.

---

*If you need assistance with the other parts of the problem (b) through (e), feel free to ask!*
**Decay Rate:** 0.0244 per year

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Calculus Questions