Tepresenting the vaide of palladium in 0.S. dollars as a runction of the time t in days.T R(t) = 30 + 50t – t2; t = 5 Find the average rates of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates.) HINT [See Example 1.] 0.1 0.01 Avg. Rate Estimate the instantaneous rate of change of R at time t, specifying the units of measurement. R'(5) = -Select-v
Tepresenting the vaide of palladium in 0.S. dollars as a runction of the time t in days.T R(t) = 30 + 50t – t2; t = 5 Find the average rates of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates.) HINT [See Example 1.] 0.1 0.01 Avg. Rate Estimate the instantaneous rate of change of R at time t, specifying the units of measurement. R'(5) = -Select-v
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 1SE: Can the average rate of change of a function be constant?
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![**Understanding the Rate of Change in the Value of Palladium**
Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of time \( t \) in days.
\[ R(t) = 30 + 50t - t^2; \, t = 5 \]
**Objective:**
Find the average rates of change of \( R(t) \) over the time intervals \([t, t + h]\), where \( t \) is as indicated and \( h = 1, 0.1, \) and \( 0.01 \) days. (Use smaller values of \( h \) to check your estimates.) HINT [See Example 1.]
**Table for Average Rate Calculation:**
| \( h \) | 1 | 0.1 | 0.01 |
|---------------|-----------|-----------|----------|
| Avg. Rate | [ ] | [ ] | [ ] |
**Task:**
Estimate the instantaneous rate of change of \( R \) at time \( t \), specifying the units of measurement.
\[ R'(5) = \text{---Select---} \]
**Instructions:**
1. Compute the average rate of change \( \frac{R(t+h) - R(t)}{h} \) for each given \( h \).
2. Use these values to estimate the instantaneous rate of change at \( t = 5 \), which involves taking the derivative and evaluating it at \( t = 5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F384c62c8-ec55-427c-bdca-bbe2475b0057%2Fb4c42958-a30e-4b62-bcb1-2fd48bf3f020%2F2esavi7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Rate of Change in the Value of Palladium**
Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of time \( t \) in days.
\[ R(t) = 30 + 50t - t^2; \, t = 5 \]
**Objective:**
Find the average rates of change of \( R(t) \) over the time intervals \([t, t + h]\), where \( t \) is as indicated and \( h = 1, 0.1, \) and \( 0.01 \) days. (Use smaller values of \( h \) to check your estimates.) HINT [See Example 1.]
**Table for Average Rate Calculation:**
| \( h \) | 1 | 0.1 | 0.01 |
|---------------|-----------|-----------|----------|
| Avg. Rate | [ ] | [ ] | [ ] |
**Task:**
Estimate the instantaneous rate of change of \( R \) at time \( t \), specifying the units of measurement.
\[ R'(5) = \text{---Select---} \]
**Instructions:**
1. Compute the average rate of change \( \frac{R(t+h) - R(t)}{h} \) for each given \( h \).
2. Use these values to estimate the instantaneous rate of change at \( t = 5 \), which involves taking the derivative and evaluating it at \( t = 5 \).
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