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Suppose that during the first few hours of a laboratory experiment, the temperature of a certain substance is closely approximated by the function f(t)-3-212+ St, where t is measured in hours, with 2-0 corresponding to the instant the experiment begins, and f(t) is the temperature (°F) of the substance after t hours. (a) Find an expression for Af/At using the interval [0, t). What are the units for Af/At? O p2/hr² OF2/min O °C/min O "F/hr O °C/hr (b) Use the result in part (a) to complete the following table. Round the answers to four decimal places. [0, 0.1) [0, 0.01] [0, 0.001] [0, 0.0001] Interval Af/At (c) In part (b), as the right-hand endpoint gets closer and closer to 0, what value does Af/At seem to be approaching? This target value tells us the rate at which the temperature is changing at the instant the experiment begins. F/hr

Suppose that during the first few hours of a laboratory experiment, the temperature of a certain substance is closely approximated by the function f(t)-3-212+ St, where t is measured in hours, with 2-0 corresponding to the instant the experiment begins, and f(t) is the temperature (°F) of the substance after t hours. (a) Find an expression for Af/At using the interval [0, t). What are the units for Af/At? O p2/hr² OF2/min O °C/min O "F/hr O °C/hr (b) Use the result in part (a) to complete the following table. Round the answers to four decimal places. [0, 0.1) [0, 0.01] [0, 0.001] [0, 0.0001] Interval Af/At (c) In part (b), as the right-hand endpoint gets closer and closer to 0, what value does Af/At seem to be approaching? This target value tells us the rate at which the temperature is changing at the instant the experiment begins. F/hr

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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Suppose that during the first few hours of a laboratory experiment, the temperature of a certain substance is closely approximated by the function f(t) = -2²+ St, where t is measured in hours, with t = 0 corresponding to the instant the experiment begins, and f(t) is the temperature (°F) of the substance after t hours. (a) Find an expression for Af/At using the interval [0, t]. What are the units for Af/At? O °F2/hr² O eF2/min O °C/min @F/hr O °C/hr (b) Use the result in part (a) to complete the following table. Round the answers to four decimal places. [0, 0.1] [0, 0.001] [0, 0.0001] Interval Af/At [0, 0.01] (c) In part (b), as the right-hand endpoint gets closer and closer to 0, what value does Af/At seem to be approaching? This target value tells us the rate at which the temperature is changing at the instant the experiment begins. °F/hr
Transcribed Image Text:Suppose that during the first few hours of a laboratory experiment, the temperature of a certain substance is closely approximated by the function f(t) = -2²+ St, where t is measured in hours, with t = 0 corresponding to the instant the experiment begins, and f(t) is the temperature (°F) of the substance after t hours. (a) Find an expression for Af/At using the interval [0, t]. What are the units for Af/At? O °F2/hr² O eF2/min O °C/min @F/hr O °C/hr (b) Use the result in part (a) to complete the following table. Round the answers to four decimal places. [0, 0.1] [0, 0.001] [0, 0.0001] Interval Af/At [0, 0.01] (c) In part (b), as the right-hand endpoint gets closer and closer to 0, what value does Af/At seem to be approaching? This target value tells us the rate at which the temperature is changing at the instant the experiment begins. °F/hr
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