You have not answered. R(t) = 340 - 0.5 Rewrite this in the form R(t) = Rgekt. Round k to 4 decimals. Ro = . and k Is this an exponential growth or exponential decay function? O A. Exponential decay OB. Exponential growth Answers
You have not answered. R(t) = 340 - 0.5 Rewrite this in the form R(t) = Rgekt. Round k to 4 decimals. Ro = . and k Is this an exponential growth or exponential decay function? O A. Exponential decay OB. Exponential growth Answers
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 Functions: Growth and Decay
**Given Function:**
\[ R(t) = 340 \cdot 0.5^t \]
**Task:**
Rewrite this function in the form:
\[ R(t) = R_0 e^{kt} \]
Round \( k \) to 4 decimal places.
* Inputs to fill:
* \( R_0 = \_\_\_\_\_ \)
* \( k = \_\_\_\_\_ \)
**Question:**
Determine whether the function represents exponential growth or decay.
- A. Exponential decay
- B. Exponential growth
**Answer Section:**
| | Answer |
|--------|--------|
| | |
| | |
| | |
**Important Note:**
When changing the base from a constant to the natural base \( e \), it is essential to determine:
- \( R_0 \) is the initial value (340 in this case).
- The constant 0.5 indicates a factor of decay, as it is less than 1.
Finally, calculate \( k \) using the properties of exponents and logarithms, particularly:
\[ 0.5 = e^k \]
Use this equation to find \( k \). Use the natural logarithm to solve for \( k \):
\[ k = \ln(0.5) \]
Once calculated, round \( k \) to four decimal places. Determine the nature of the function based on the value of the base (in this case, decay because 0.5 < 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71937467-3418-4168-ba3a-1f533ed3f436%2Fa0234d9c-800c-47ef-91bd-6d415459efb2%2Fkvewagd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponential Functions: Growth and Decay
**Given Function:**
\[ R(t) = 340 \cdot 0.5^t \]
**Task:**
Rewrite this function in the form:
\[ R(t) = R_0 e^{kt} \]
Round \( k \) to 4 decimal places.
* Inputs to fill:
* \( R_0 = \_\_\_\_\_ \)
* \( k = \_\_\_\_\_ \)
**Question:**
Determine whether the function represents exponential growth or decay.
- A. Exponential decay
- B. Exponential growth
**Answer Section:**
| | Answer |
|--------|--------|
| | |
| | |
| | |
**Important Note:**
When changing the base from a constant to the natural base \( e \), it is essential to determine:
- \( R_0 \) is the initial value (340 in this case).
- The constant 0.5 indicates a factor of decay, as it is less than 1.
Finally, calculate \( k \) using the properties of exponents and logarithms, particularly:
\[ 0.5 = e^k \]
Use this equation to find \( k \). Use the natural logarithm to solve for \( k \):
\[ k = \ln(0.5) \]
Once calculated, round \( k \) to four decimal places. Determine the nature of the function based on the value of the base (in this case, decay because 0.5 < 1).
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