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Denise brews a cup of coffee and leaves it in a room at a constant 20°C. She uses a temperature probe to record the coffee’s temperature every 4 minutes, obtaining the following data:
After graphing the data, Denise believes a suitable model will be T=20+abt,a,b∈R.
Explain why T−20 can be modeled by an exponential function.
Find the equation of the least squares exponential regression curve for T−20.
Write down the coefficient of determination, R2.
Interpret what the value of R2 implies about the model.
Hence predict the temperature of the coffee after 14 minutes.
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