2. The rate at which a phase transformation proceeds depends on the time t and the dt transformed volume fraction (quantity) y of the product, according to dy = 4kt° (1– y) dt where k is a constant. At the start of the phase transformation, the amount of transformed product is zero: y(0) =0. Determine the transformed fraction as a function y(t) of the time t.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. The rate
at which a phase transformation proceeds depends on the time t and the
dt
transformed volume fraction (quantity) y of the product, according to
dy
4kt (1– y)
dt
where k is a constant. At the start of the phase transformation, the amount of transformed
product is zero: y(0) = 0. Determine the transformed fraction as a function y(t) of the time t.
If k = 0.002, determine the amount of transformed fraction at t= 5s.
Transcribed Image Text:2. The rate at which a phase transformation proceeds depends on the time t and the dt transformed volume fraction (quantity) y of the product, according to dy 4kt (1– y) dt where k is a constant. At the start of the phase transformation, the amount of transformed product is zero: y(0) = 0. Determine the transformed fraction as a function y(t) of the time t. If k = 0.002, determine the amount of transformed fraction at t= 5s.
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