Select the correct answer from each drop-down menu.
Let [tex]$b(t)$[/tex] be the number of unread books remaining on Alex's bookshelf after reading consistently for [tex]$t$[/tex] months.
[tex]$b(t)=75-5 t$[/tex]
So, [tex]$b(9)=[/tex] ____. This means that ____, the ____
Answer (1)
Calculate b ( 9 ) by substituting t = 9 into the equation b ( t ) = 75 − 5 t .
Find b ( 9 ) = 75 − 5 ( 9 ) = 30 .
Interpret b ( 9 ) = 30 as the number of unread books remaining after 9 months.
Conclude that b ( 9 ) represents the number of unread books.
Explanation
Calculate b(9) First, we need to calculate b ( 9 ) . We are given the function b ( t ) = 75 − 5 t , which represents the number of unread books remaining on Alex's bookshelf after reading consistently for t months. To find b ( 9 ) , we substitute t = 9 into the equation.
Substitution and Calculation Now, let's substitute t = 9 into the equation: b ( 9 ) = 75 − 5 ( 9 ) b ( 9 ) = 75 − 45 b ( 9 ) = 30
Interpretation of the Result So, b ( 9 ) = 30 . This means that after 9 months, Alex has 30 unread books remaining on his bookshelf. The function b ( t ) represents the number of unread books.
Examples
Understanding how quickly you consume books can help you plan your reading habits and budget. For example, if you know you read 5 books a month, you can estimate how many books you'll read in a year and adjust your book purchases accordingly. This simple linear model helps in predicting future reading habits and managing resources effectively.
