Question

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes.What best describes thiz ?

Answer 1

Answer: We know that an "exponential growth" is that where a function start growing slowly and after start increasing more quickly.

a "logarithmic growth" is the opposite of this, at first you will see a quick increase, that after some time gets slower.

But in this case we are searching for decays: The decays are the opposite of the growths, an "logarithmic decay" starts slow and gets faster latter, and an "exponential decay" decreases very quickly at first, and latter more slowly.

Then, the model for the temperature of the hot tea over the time is a "exponential decay", this is a function of the form T(x) = T₀$e^{-kt}$, where T₀ is the initial temperature, t is the time, and k is a constant number.