A chilled bottle of water is placed in a warm office where the air temperature is
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
A chilled bottle of water is placed in a warm office where the air temperature is 24∘C. Its initial temperature is 8∘C. The table shows temperature readings of the bottle over the next several minutes.
Time t (min): 0, 3, 6, 9, 12
Temperature T (∘C): 8.0, 10.7, 13.6, 16.2, 18.4
(a) Verify that the data are consistent with an exponential approach toward 24∘C by transforming the temperature readings to a linear relationship in t and determining a line of best fit.
(b) Use your linear model from part (a) to estimate the proportionality constant k (in min−1) for the warming bottle.
(c) Using the estimated value of k, determine the time, to the nearest tenth of a minute, required for the bottle to warm to 20∘C.
(d) Discuss one possible reason, grounded in physical considerations, why the actual time observed in an experiment might differ from the model’s prediction.