(a) An object with the initial temperature To is placed in a tank of water, the temperature of which is kep at 15°C. After 25 minutes the temperature of the object is 178°C, and after 50 minutes it is 89°C. (i) Presuming that Newton's law of cooling applies, what is the initial value of To? (ii) How long does it take for the object to cool to 70°C?
(a) An object with the initial temperature To is placed in a tank of water, the temperature of which is kep at 15°C. After 25 minutes the temperature of the object is 178°C, and after 50 minutes it is 89°C. (i) Presuming that Newton's law of cooling applies, what is the initial value of To? (ii) How long does it take for the object to cool to 70°C?
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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Transcribed Image Text:QUESTION 3
(a) An object with the initial temperature To is placed in a tank of water, the temperature of which is kept
at 15°C. After 25 minutes the temperature of the object is 178°C, and after 50 minutes it is 89°C.
(i) Presuming that Newton's law of cooling applies, what is the initial value of To?
(ii) How long does it take for the object to cool to 70°C?
(b) Suppose that a radioactive metal has a half-life of 5000 years. If today, only 35 grams of a metal remains,
(i) When was there 170 grams of the metal?
(ii) When will there be only 19 g left of the metal?
(c) Silkworms are being bred in an enclosure that holds a maximum of 750 silkworms in order to produce
silk fabric. If the population grows according to the Malthusian model, with a growth constant k = 0,05
when time is measured in days, how long will it take for an initial population of 50 silkworms to multiply
until the enclosure is full?
(d) A variable R(t), t20 obeys the differential equation
dR
dt
(R²
(R²
(i) Determine the equilibrium points of the model.
+5R+1)(e-7) (22R-4-52-R).
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