Solution
Step 1:
At t = 0 minute, the temperature is 450
[tex]\begin{gathered} At\text{ t = 0 minute , the temperature is 450}^of \\ \text{At t = 5 minutes , the temperature is 300}^of \end{gathered}[/tex][tex]\begin{gathered} \text{Rate of change, slope = }\frac{300\text{ - 450}}{5\text{ - 0}} \\ Slope\text{ = }\frac{-150}{5}\text{ = -30}^of\text{ min}^{-1} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} \text{y = mx + c} \\ \text{y = -30x + 450} \\ \text{x is the time in minutes} \\ \text{y is temperature in }^of \end{gathered}[/tex]a)
[tex]\begin{gathered} \text{y = 130}^of\text{ , x = ?} \\ 130\text{ = -30x + 450} \\ 30x\text{ = 450 - 130} \\ 30x\text{ = 320} \\ \text{x = }\frac{320}{30} \\ \text{x = }\frac{32}{3} \\ x\text{ = 10minutes 40 seconds} \\ 7:10\text{ :40 pm} \end{gathered}[/tex]b)
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