Question

functions and lines finding inputs and outputs of a two - step function that models a real - worl... carmen wants to save $900 to buy a tv. she saves $18 each week. the amount, a (in dollars), that she still needs after w weeks is given by the following function. \\(a(w)=900 - 18w\\) answer the following questions. (a) if carmen still needs $558, how many weeks has she been saving? weeks (b) how much money does carmen still need after 5 weeks? $

Explanation:

Part (a)

Step1: Set up the equation

We know the function \( A(w)=900 - 18w \), and we are given that \( A(w) = 558 \). So we set up the equation \( 900-18w=558 \).

Step2: Solve for \( w \)

Subtract 900 from both sides: \( - 18w=558 - 900=-342 \).
Then divide both sides by - 18: \( w=\frac{-342}{-18} = 19 \).

Part (b)

Step1: Substitute \( w = 5 \) into the function

We have the function \( A(w)=900 - 18w \). Substitute \( w = 5 \) into it: \( A(5)=900-18\times5 \).

Step2: Calculate the value

First, calculate \( 18\times5 = 90 \). Then, \( A(5)=900 - 90=810 \).

Answer:

(a) \( 19 \) weeks
(b) \( \$810 \)