-kt Newton's law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T (t) is modeled by T (t)=T+(To-Ta)e In this model, T represents the temperature of the surrounding air, To represents the initial temperature of the object, and it is the time after the object starts cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. Water in a water heater is originally 128°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 64°F. The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00354. (a) Write a function that models the temperature T (t) (in °F) of the water t hours after the water heater is shut off. (b) What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. (c) Dominic does not like to shower with water less than 121°F. If Dominic waits 24 hr, will the water still be warm enough for the shower? Round to the nearest degree.
-kt Newton's law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature T (t) is modeled by T (t)=T+(To-Ta)e In this model, T represents the temperature of the surrounding air, To represents the initial temperature of the object, and it is the time after the object starts cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. Water in a water heater is originally 128°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 64°F. The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00354. (a) Write a function that models the temperature T (t) (in °F) of the water t hours after the water heater is shut off. (b) What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. (c) Dominic does not like to shower with water less than 121°F. If Dominic waits 24 hr, will the water still be warm enough for the shower? Round to the nearest degree.
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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1) the model for the temperature of water is T(t)=?
2) The temperatilure of the water after 12hr the heater is shut off?
3) Temperature after 24hr will be?
Transcribed Image Text:-kt
Newton's law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will
approach the temperature of the surrounding air. The temperature I (t) is modeled by T (t)=T+(To-Ta)e . In this model, T represents the temperature
of the surrounding air, To represents the initial temperature of the object, and it is the time after the object starts cooling. The value of k is a constant of
proportion relating the temperature of the object to its rate of temperature change.
Water in a water heater is originally 128°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 64°F. The water
cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00354.
(a) Write a function that models the temperature T (t) (in °F) of the water t hours after the water heater is shut off.
(b) What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree.
(c) Dominic does not like to shower with water less than 121°F. If Dominic waits 24 hr, will the water still be warm enough for the shower? Round to the nearest
degree.
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