Question

The temperature of an object in degrees Fahrenheit after t minutes is represented by the equation T(t)=(61(e^(-0.0174t))+75. What is the temperature of the metal after 1 hour and 30 minutes: Round the answer to the nearest whole number.

Answer 1

Given that 1 hour and 30 minutes can be expressed as 90 minutes, then we can replace t=90 in the equation to find the temperature. Doing so, we have:

`\begin{gathered} T(t)=61e^(-0.0174t)+75. \\ T(90)=61e^(-0.0174(90))+75.\text{ (Replacing)} \end{gathered}`

`\begin{gathered} T(90)=61e^(-1.566)^{}+75.(\text{ Multiplying)} \\ T(90)=61\cdot0.209+75\text{ (Raising e to the power of -1.566)} \\ T(90)=12.74+75\text{ (Multiplying)} \\ T(90)=87.74\text{ (Adding)} \end{gathered}`

The answer would be 88 in degrees Farenheit. (Rounding to the nearest whole number)