A hiker starts climbing a hill from an elevation of 200 feet 200~\text{feet} 200 feet above sea level. After 20 minutes 20~\text{minutes} 20 minutes , the hiker reaches an elevation of 800 feet 800~\text{feet} 800 feet above sea level. Let h ( t ) h\left(t\right) h ( t ) represent the elevation (in feet) above sea level of the hiker t t t minutes after starting the climb. Evaluate h ( 20 ) − h ( 0 ) 20 − 0 \frac{h\left(20\right)-h\left(0\right)}{20-0} 20 − 0 h ( 20 ) − h ( 0 ) and select the correct interpretation of this quotient.

30 ft/min 30~\text{ft/min} 30 ft/min , The hiker climbs at an average rate of 30 ft/min 30~\text{ft/min} 30 ft/min during the first 20 minutes 20~\text{minutes} 20 minutes of the hike.

30 ft/min 30~\text{ft/min} 30 ft/min , The hiker climbs at an average rate of 30 ft/min 30~\text{ft/min} 30 ft/min during the last 20 minutes 20~\text{minutes} 20 minutes of the hike.

6 ft/min 6~\text{ft/min} 6 ft/min , The hiker climbs at an average rate of 6 ft/min 6~\text{ft/min} 6 ft/min during the first 20 minutes 20~\text{minutes} 20 minutes of the hike.

20 ft/min 20~\text{ft/min} 20 ft/min , The hiker climbs at an average rate of 20 ft/min 20~\text{ft/min} 20 ft/min during the first 20 minutes 20~\text{minutes} 20 minutes of the hike.

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0. Functions(0)
1. Limits and Continuity(0)
2. Intro to Derivatives(0)
3. Techniques of Differentiation(0)
4. Applications of Derivatives(0)
5. Graphical Applications of Derivatives(0)
6. Derivatives of Inverse, Exponential, & Logarithmic Functions(0)
7. Antiderivatives & Indefinite Integrals(0)
8. Definite Integrals(0)

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27PRACTICE PROBLEM

A hiker starts climbing a hill from an elevation of $200~\text{feet}$ above sea level. After $20~\text{minutes}$ , the hiker reaches an elevation of $800~\text{feet}$ above sea level. Let $h\left(t\right)$ represent the elevation (in feet) above sea level of the hiker $t$ minutes after starting the climb. Evaluate $\frac{h\left(20\right)-h\left(0\right)}{20-0}$ and select the correct interpretation of this quotient.

ANSWERS OPTIONS

$30~\text{ft/min}$ , The hiker climbs at an average rate of $30~\text{ft/min}$ during the last $20~\text{minutes}$ of the hike.

$6~\text{ft/min}$ , The hiker climbs at an average rate of $6~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.

$30~\text{ft/min}$ , The hiker climbs at an average rate of $30~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.

$20~\text{ft/min}$ , The hiker climbs at an average rate of $20~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.

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