Question15. Water whose temperature is at $100^{\circ} \mathrm{C}$ is left to cool in a room where the temperature is $30^{\circ} \mathrm{C}$ . After 2 minutes, the water temperature is $88^{\circ} \mathrm{C}$ . If the water temperature $T$ is a function of time $t$ given by $T=30+70 e^{k t}$ , find $k$ . Round your answer to the nearest hundredth.

Studdy Solution
Calculate the value of $k$ and round to the nearest hundredth:
$k \approx \frac{1}{2} \ln\left(\frac{58}{70}\right) \approx \frac{1}{2} \times (-0.2070) \approx -0.1035$
Rounded to the nearest hundredth, $k \approx -0.10$ .
The value of $k$ is:
$\boxed{-0.10}$

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