Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - 2.1 Exercises - Page 159: 95

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: $d = 2t,~~~~~0 \leq t \lt 120$ $d = 240+4(t-120),~~~~~120 \leq t \lt 320$ $d = 1040+7(t-320),~~~~~320 \leq t \leq 370$
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