Question

Isaac Newton proved that fluids cool exponentially when left out in an open space. A cup of coffee was poured at a
temperature of 210°F and left on the dining room table to cool. If you start drinking it at a temperature of 150°F, 10 minutes
later, what will be the temperature be when you take the last sip 18 minutes after you poured it?

Answer 1

The temperature will be when you take the last sip 18 minutes after you poured it, will be 114.64 °F.

What is an exponent?

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

Isaac Newton proved that fluids cool exponentially when left out in an open space.

A cup of coffee was poured at a temperature of 210°F and left on the dining room table to cool.

If you start drinking it at a temperature of 150°F, 10 minutes later.

The exponential function is given as

$\rm T_f = T_i (a)^{-t}$

Then the initial temperature will be 210°F.

$\begin{aligned} 150 &= \rm 210 (a)^{-10}\\\\0.7143 &= \rm a^{-10}\\\\-0.146 &= \rm -10 \log a\\\\0.0146 &= \rm \log a\\\\\rm a &= \rm 1.0342 \end{aligned}$

Then the equation will be

$\rm T_f = 210 (1.0342)^{-t}$

Then the temperature will be when you take the last sip 18 minutes after you poured it.

$\rm T_f = 210 (1.0342)^{-18}\\\\T_f = 114.64 \ ^oF$

More about the exponent link is given below.

https://brainly.com/question/5497425

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