Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises: 17

Answer

\[In\,year\,\,\,2030\,population\,\,will\,be\,\,860\]

Work Step by Step

\[\begin{gathered} General\,form\,of\,linear\,function\,is\, \hfill \\ \, \hfill \\ y = mx + b \hfill \\ \hfill \\ or \hfill \\ \hfill \\ p\,\left( t \right) = mt + l \hfill \\ \hfill \\ we\,\,\,want\,\,growing\,\,rate\,of\,24\,people\,\,per\,year \hfill \\ so\,slope\,of\,the\,function\,\,is\,\, \hfill \\ \hfill \\ m = 24 \hfill \\ \hfill \\ population\,in\,year\,2015\,was\,500\,,\,so\,\,we\,\,\,want\,\,p\,\left( 0 \right) = 500 \hfill \\ because\,t = 0\,\,represents\,yars\,2015.{\text{ }}use\,\,\,this\,information\,to\,find\,l \hfill \\ \hfill \\ 500 = 24t + l \hfill \\ \hfill \\ substitute\,\,\,t = 0 \hfill \\ \hfill \\ 500 = 24 \cdot 0 + l \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ l = 500 \hfill \\ \hfill \\ then,\,function\,that\,models\,\,population\,is \hfill \\ \hfill \\ p\,\left( t \right) = 24t + 500 \hfill \\ \hfill \\ year\,\,\,2030\,is\,represented\,\,with\,t = 15\,,\,so\,prediction\,is: \hfill \\ \hfill \\ p\,\left( {15} \right) = 24 \cdot 15 + 500 = 860 \hfill \\ \hfill \\ the\,\,solution\,\,\,is \hfill \\ \hfill \\ p\,\left( t \right) = 24t + 500 \hfill \\ \hfill \\ In\,year\,\,\,2030\,population\,will\,be\,\,860 \hfill \\ \hfill \\ \end{gathered} \]
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