Consider the following problem:The temperature of a cup of cocoa is decreasing at a rate of r(t)=−5.5e−0.09t degrees Celsius per minute (where t is the time in minutes). At time t=2, the temperature of the cocoa is 72 degrees Celsius. What is the temperature of the cocoa at t=10 minutes?Which expression can we use to solve the problem?Choose 1 answer:(A) ∫210r(t)dt+72(B) ∫r(t)dt+72(C) ∫r(t)dt(D) ∫210r(t)dt
Q. Consider the following problem:The temperature of a cup of cocoa is decreasing at a rate of r(t)=−5.5e−0.09t degrees Celsius per minute (where t is the time in minutes). At time t=2, the temperature of the cocoa is 72 degrees Celsius. What is the temperature of the cocoa at t=10 minutes?Which expression can we use to solve the problem?Choose 1 answer:(A) ∫210r(t)dt+72(B) ∫r(t)dt+72(C) ∫r(t)dt(D) ∫210r(t)dt
Integrate Rate of Change: To find the temperature of the cocoa at t=10 minutes, we need to integrate the rate of temperature change from t=2 to t=10 and add this to the initial temperature at t=2.
Calculate Change in Temperature: The rate of temperature change is given by r(t)=−5.5e(−0.09t). To find the change in temperature from t=2 to t=10, we need to integrate r(t) with respect to t from 2 to 10.
Find Total Temperature Change: The integral of r(t) from t=2 to t=10 will give us the total change in temperature over this time period. Since we are given the temperature at t=2, we will add this change to 72 degrees Celsius to find the temperature at t=10.
Use Correct Expression: The correct expression to use for this problem is the definite integral of r(t) from t=2 to t=10, plus the initial temperature at t=2. This corresponds to choice (A) ∫210r(t)dt+72.
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