**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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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

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

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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Question

**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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