Question

PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT

Answer 1

Since the room temperature is 22 degrees Celsius,

`(dT)/(dt)=k(T-22)`

Solving the differential equation,

`(1)/(T-22) dT=k dt \\ \\ \int (1)/(T-22) dT=\int k dt \\ \\ \ln|T-22|=kt+C`

When t=0, the temperature is 100 degrees.

`\ln 78=C \\ \\ \implies \ln|T-22|=kt+\ln 78`

When t=1, the temperature is 80 degrees.

`\ln 58=k+\ln 78 \implies k=\ln(29/39) \\ \\ \implies \ln|T-22|=t \ln(29/39)+\ln 78`

Setting t=4,

`\ln|T-22|=4\ln(29/39)+\ln 78 \\ \\ T=22+e^(4\ln(29/39)+\ln 78) \approx \boxed{46}`