Learning Diagnostic Analytics Recommendations Skill plans Math Common Core You have prizes Algebra 2 > T.12 Exponential growth and decay: word problems TYQ You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes? grams Submit
Learning Diagnostic Analytics Recommendations Skill plans Math Common Core You have prizes Algebra 2 > T.12 Exponential growth and decay: word problems TYQ You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes? grams Submit
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Exponential Growth and Decay: Word Problems
#### Algebra 2
#### T.12 Exponential Growth and Decay: Word Problems
**Problem:**
You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes?
**Answer Box:**
```
[ ] grams
```
**Actions:**
- After entering your answer, click the "Submit" button.
**Concept Explanation:**
To solve this problem, use the formula for exponential decay:
\[ N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the substance after time \( t \).
- \( N_0 \) is the original quantity of the substance.
- \( t \) is the elapsed time.
- \( t_{1/2} \) is the half-life of the substance.
For this problem:
- \( N_0 = 8,560 \) grams.
- \( t = 45 \) minutes.
- \( t_{1/2} = 15 \) minutes.
Using the formula, we can calculate the remaining quantity of rubidium after 45 minutes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24eec1a8-f950-42bd-9025-df0c53fe3ee6%2Ffeb5edeb-e4d1-436c-bd5d-16dfa2100e33%2F32tn0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponential Growth and Decay: Word Problems
#### Algebra 2
#### T.12 Exponential Growth and Decay: Word Problems
**Problem:**
You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes?
**Answer Box:**
```
[ ] grams
```
**Actions:**
- After entering your answer, click the "Submit" button.
**Concept Explanation:**
To solve this problem, use the formula for exponential decay:
\[ N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the substance after time \( t \).
- \( N_0 \) is the original quantity of the substance.
- \( t \) is the elapsed time.
- \( t_{1/2} \) is the half-life of the substance.
For this problem:
- \( N_0 = 8,560 \) grams.
- \( t = 45 \) minutes.
- \( t_{1/2} = 15 \) minutes.
Using the formula, we can calculate the remaining quantity of rubidium after 45 minutes.
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