# Chapter 1 - Problems: 56

$T = 104.5^{\circ}F$

#### Work Step by Step

We can write a linear equation in this form: $T = mt+T_0$ $m$ is the slope of the line $t$ is the time in hours after 8:05 am $T_0$ is the temperature at 8:05 am We can find the slope $m$: $m = \frac{\Delta T}{\Delta t}$ $m = \frac{101.0^{\circ}F-97.0^{\circ}F}{12:05~pm-8:05~pm}$ $m = \frac{4.0^{\circ}~F}{4~hr}$ $m = 1.0^{\circ}F/hr$ We can write the linear equation: $T = 1.0~t+97.0^{\circ}F$ 3:35 pm is 7.5 hours after 8:05 am. We can find the temperature at 3:35 pm: $T = 1.0~t+97.0^{\circ}~F$ $T = (1.0^{\circ}F/hr)(7.5~hr)+97.0^{\circ}~F$ $T = 104.5^{\circ}F$

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