Math Problem Statement
The temperature of water in an urn is increasing at a rate of r(t) = 21e^(−0.4t) degrees Celsius per minute, where t is the time in minutes. At time t = 0 minutes, the temperature of the water is 16 degrees Celsius. (a) Solve the defnite integral ∫ 8 0 r(t) dt to find out how much the temperature increased between t = 0 and t = 8 minutes.
Solution
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Math Problem Analysis
Mathematical Concepts
Definite Integrals
Exponential Functions
Rate of Change
Formulas
∫ e^(ax) dx = (1/a)e^(ax)
∫ 21e^(-0.4t) dt = -52.5e^(-0.4t)
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12
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