Question

olivia receives a prepaid card worth $180 to buy books. each book she purchases costs $20. the function b(x)=180 - 20x represents the amount of money, b, in dollars, remaining on the card after buying x books. a. find f(0). y = 180 b(0)=180 - 20×0 b(0)=180 - 0 = 180 b. what key feature is f(0)? what is the meaning within the context? c. find f(x)=0.

Explanation:

Step1: Evaluate $f(0)$

Given $f(x)=180 - 20x$, substitute $x = 0$. So $f(0)=180-20\times0=180$. This means when no books are bought ($x = 0$), the amount of money remaining on the card is $180$ dollars.

Step2: Analyze the meaning of $f(0)$

In the context of buying books with a prepaid - card, $f(0)$ represents the initial amount of money on the card, which is $\$180$.

Step3: Solve for $x$ when $f(x)=0$

Set $f(x)=0$, so $180 - 20x=0$. Add $20x$ to both sides: $180=20x$. Then divide both sides by $20$: $x=\frac{180}{20}=9$. This means when $9$ books are bought, the money on the card is used up.

Answer:

a. $f(0)=180$. It means the initial amount of money on the prepaid card is $\$180$ when no books are bought.
b. $f(0)$ represents the initial value of the function. In the context, it is the starting amount of money on the card, which is $\$180$.
c. When $f(x)=0$, $x = 9$. This means that after buying $9$ books, the amount of money remaining on the card is $0$ dollars.