Question

name: jaydeci
1.11 formative assessment (a)
suppose that you decide to participate in a charity walkathon to raise money for your cause. some
people decide to donate a fixed amount, while others agree to donate a little money for every mile you
walk. before the event starts, you raised $25, and you have been pledged $1.50 for each mile you
walk. the function defined by ( d(w)=1.5w + 25 ) can be used to relate the miles you walk, ( w ), and the
amount of money donated to you in dollars, ( d(w) ).
(a) evaluate ( d(3) ), and explain what it means in the context of the problem.
( d(3)=1.53 + 25 )
(b) while you were walking, you lost track of the number of miles you had walked. at the end of
the event, an organizer tells you that you raised $40 through your walk. how many miles did
you walk?
name jaydeci cruz
1.10 - 1.11 quiz a
period

1. a function is

1 point
(a) a graph that is a straight line
(b) a relationship that goes through the origin
(c) a relationship where each input matches to exactly one output
(d) a relationship where an input can have multiple outputs

1. does the graph represent a linear or nonlinear function?

1 point
how do you know?

1. mr. nickerson is saving money for a new fishing rod. he has $80 in his bank account and is saving

$20 per month. the situation is modeled by the following function where ( x ) is the number of months:
1 point each
( f(x)=20x + 80 )
(a) find ( f(5) )
( f(5)=20(5)+80 )
( 20x + 80 = 240 )
( f(5)=180 )
(b) what does ( f(5) ) mean in context of the problem?
the total money mr. nickerson has saved
for after 5 months
(c) find ( x ) if ( f(x)=240 )
(d) if the fishing rod costs $360, how many months will mr. nickerson have to save?

Explanation:

Step1: Evaluate \(d(3)\)

Substitute \(w = 3\) into the function \(d(w)=1.5w + 25\).
\(d(3)=1.5\times3+25\)
\(=4.5 + 25\)
\(=29.5\)
This means that if you walk \(3\) miles, the amount of money donated to you is \(\$29.5\).

Step2: Find the number of miles walked when \(d(w) = 40\)

Set up the equation \(1.5w+25 = 40\).
Subtract \(25\) from both sides: \(1.5w=40 - 25\)
\(1.5w=15\)
Divide both sides by \(1.5\): \(w=\frac{15}{1.5}\)
\(w = 10\)

Step3: Answer question 1

A function is a relationship where each input matches to exactly one output. So the answer is c.

Step4: Answer question 2

The graph is a linear function because it is a straight line.

Step5: Evaluate \(f(5)\) for \(f(x)=20x + 80\)

Substitute \(x = 5\) into the function: \(f(5)=20\times5+80\)
\(=100+80\)
\(=180\)

Step6: Explain \(f(5)\) in context

\(f(5)\) means the total amount of money Mr. Nickerson has saved after \(5\) months.

Step7: Find \(x\) when \(f(x)=240\)

Set up the equation \(20x + 80=240\).
Subtract \(80\) from both sides: \(20x=240 - 80\)
\(20x=160\)
Divide both sides by \(20\): \(x=\frac{160}{20}\)
\(x = 8\)

Step8: Find the number of months to save \(\$360\)

Set up the equation \(20x+80 = 360\).
Subtract \(80\) from both sides: \(20x=360 - 80\)
\(20x=280\)
Divide both sides by \(20\): \(x=\frac{280}{20}\)
\(x = 14\)

Answer:

(a) \(d(3)=29.5\), meaning \(\$29.5\) is donated when \(3\) miles are walked. (b) \(10\) miles. (1) c. (2) Linear function (because it's a straight line). (3a) \(180\). (3b) Total money saved after \(5\) months. (3c) \(8\). (3d) \(14\) months.