Question

Can you help me with the letter a and b please

Answer 1

`\begin{gathered} A)183^(\circ)F \\ b)t=19.33296\approx19.3\:minutes \end{gathered}`

1) Note that this is an exponential function.

a) Let's find this initial temperature algebraically, we need to consider that the temperature of that coffee by the time it was handed out was measured for the instant of time t=0

`\begin{gathered} C(t)=108e^(-0.08t)+75 \\ C(0)=108e^(-0.08\cdot0)+75 \\ C(0)=108\cdot\:1+75 \\ C(0)=183^(\circ)F \end{gathered}`

b) Now, for part B we know that the final temperature is 98º. So, we can write out the following:

`\begin{gathered} C(t)=108e^(-0.08t)+75 \\ 98=108e^(-0.08t)+75 \\ 108e^{\left\{-0.08t\right\}}+75=98 \\ 108e^{\left\{-0.08t\right\}}=23 \\ ln(108e^{\left\{-0.08t\right\}})=ln(23) \\ t=-(\ln \left((23)/(108)\right))/(0.08) \\ t=19.33296 \end{gathered}`

Approximately 19 minutes