Question

Marcos purchases a top-up card for his pre-paid cell phone. His remaining balance, B, can be modeled by the equation B=40−0.1n, where n is the number of minutes he's talked since purchasing the card.
a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?

b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?

c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?

Answer 1

Answer:

Part a) When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

part c) The slope of the equation is -0.1 and the units are dollars per minute

Step-by-step explanation:

we have

$B=40-0.1n$

where

B is balance in dollars on the card

n is the number of minutes

Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?

we know that

The B-intercept is the value of B when the value of n is equal to zero

so

For n=0

substitute and find the value of B

$B=40-0.1(0)=\ 40$

therefore

When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?

we know that

The n-intercept is the value of n when the value of B is equal to zero

so

For B=0

substitute and find the value of n

$0=40-0.1n$

$0.1n=40$

$n=400\ minutes$

therefore

Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?

we have

$B=40-0.1n$

This is is the equation of the line into slope intercept form

$m=-0.1\frac{\ }{minute}$ -----> slope of the equation

$b=40$ ------> the B-intercept

The units of the slope are dollars per minute