Question

I need help on this question on solving it step by step thank you!

Answer 1

Answer:

It will take 83.75 minutes

Step-by-step explanation:

The initial temperature of the pop, T₀ = 45 degrees F

Temperature of the pop after 34 minutes, T = 60 degrees F

Time, t = 34 minutes

The temperature of the car, A = 108 degrees F

`\begin{gathered} (T-A)/(T_0-A)=e^(-kt) \\ \\ (60-108)/(45-108)=e^(-34t) \\ \\ 0.76=e^(-34t) \\ \\ ln0.76=-34t \\ \\ -0.274=-34k \\ \\ k=-(0.274)/(-34) \\ \\ k=0.008 \end{gathered}`

If the final temperature, T = 75.75 degrees F

`\begin{gathered} (75.75-108)/(45-108)=e^(-0.008t) \\ \\ 0.51=e^(-0.008t) \\ \\ ln0.51=-0.008t \\ \\ -0.67=-0.008t \\ \\ t=(-0.67)/(-0.008) \\ \\ t=83.75 \end{gathered}`

It will take 83.75 minutes