A hot liquid was left to cool according to the equation $T={{\mathrm{e}}^{4.5-0.1t}}$, where

Question

A hot liquid was left to cool according to the equation $T={{\mathrm{e}}^{4.5-0.1t}}$, where $T$ is the temperature of the liquid after $t$ minutes. After the liquid is cooled to $a{}^\circ $C for $b$ minutes, it is then immediately heated again according to the equation $T={{\mathrm{e}}^{0.5t-2.7}}$. State the initial temperature of the liquid when it was left to cool. Find the values of $a$ and $b$.

Accepted Answer

(i) $90.0^\circ\text{C}$; (ii) $a=27.1$, $b=12$

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

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