Answer
Example 1: We start with a block of ice at a temperature of $-12^{\circ}C$. We heat the ice at a rate of 1 degree Celsius per minute. At zero degrees, the ice melts and it takes five minutes to melt. We then heat the water for 20 minutes at a rate of two degrees Celsius per minute.
We can use a piecewise defined equation to model the temperature $T$ at time $t$, where $t$ is in minutes.
Example 2: Julia leaves home and walks toward her school at a speed of 2 m/s for 120 seconds. She then jogs at a speed of 4 m/s for 200 seconds. Julia then decides to run quickly at a speed of 7 m/s for the final 50 seconds.
We can use a piecewise defined equation to model Julia's speed $v$ at time $t$, where $t$ is in seconds.
Work Step by Step
Example 1: We start with a block of ice at a temperature of $-12^{\circ}C$. We heat the ice at a rate of 1 degree Celsius per minute. At zero degrees, the ice melts and it takes five minutes to melt. We then heat the water for 20 minutes at a rate of two degrees Celsius per minute.
We can use a piecewise defined equation to model the temperature $T$ at time $t$, where $t$ is in minutes:
$T = t-12,~~~~~0 \leq t \lt 12$
$T = 0,~~~~~12 \leq t \lt 17$
$T = 2(t-17),~~~~~17 \leq t \leq 37$
Example 2: Julia leaves home and walks toward her school at a speed of 2 m/s for 120 seconds. She then jogs at a speed of 4 m/s for 200 seconds. Julia then decides to run quickly at a speed of 7 m/s for the final 50 seconds.
We can use a piecewise defined equation to model Julia's speed $v$ at time $t$, where $t$ is in seconds:
$v = 2,~~~~~0 \leq t \lt 120$
$v = 4,~~~~~120 \leq t \lt 320$
$v = 7,~~~~~320 \leq t \leq 370$
We can use a piecewise defined equation to model Julia's distance $d$ from home at time $t$, where $t$ is in seconds:
$d = 2t,~~~~~0 \leq t \lt 120$
$d = 240+4(t-120),~~~~~120 \leq t \lt 320$
$d = 1040+7(t-320),~~~~~320 \leq t \leq 370$