sume that temperature, $T$, in degrees Fahrenheit of a roast placed in a hot oven is a linear function of, $m$, time in minutes since the roast was put in the oven.
a) Whrit does it mean to write: $T(20)=152$ ?
I want you to explain this using an English sentence.
b) Assume I also tell you that $\mathrm{T}(30)=192$. Express the Temperature after $\mathrm{m}$ minutes as a function $\mathrm{T}(\mathrm{m})$.
c) Grajh the function. What does the $y$-intercept represent? What does the slope represent?
d) Assume that the roast is done at $310^{\circ} \mathrm{F}$. How long should it stay in the oven?
Answer
\(\boxed{T(m) = 4m + 72}\) is the final answer.
Step 1 ：We are given two points on the line that describes the temperature of the roast as a function of time: (20, 152) and (30, 192).
Step 2 ：We can use these two points to find the slope of the line, which represents the change in temperature per minute. The slope is calculated as \(\frac{192-152}{30-20} = 4.0\).
Step 3 ：Once we have the slope, we can use one of the points to find the y-intercept, which represents the temperature of the roast when it was first put in the oven. The y-intercept is calculated as \(152 - 4 \times 20 = 72.0\).
Step 4 ：Therefore, the function T(m) that describes the temperature of the roast as a function of time is \(T(m) = 4m + 72\).
Step 5 ：\(\boxed{T(m) = 4m + 72}\) is the final answer.
