I’m losing

you are trying to decide which cell phone plan to purchase. plan a chargeres $40 for a new phone and $20 a month for usage. plan b provides the phone for free, but has a fee of $30 a month for usage.
use the substitution method to determine when the two plans will cost the same.

Step-by-step explanation:

In 4 months the two plans will cost the same.

Step-by-step explanation:

Let represent the number of months of usage of phone

Let represent the total amount charged by the plans.

Plan A:

Plan A charges $40 for a new phone and $20 for per month usage.

Fixed charge = $40

Per month usage charge = $20

Usage charges in dollars for months will be =

Thus total charges in dollars can be given as:

A)

Plan B.

Plan B provides the phone for free, but has a fee of $30 for per month usage.

Fixed charge = $0

Per month usage charge = $30

Usage charges in dollars for months will be =

Thus total charges in dollars can be given as:

B)

In order to determine the number of month in which the two plans will charge same we will equate the equations.

Substituting equation B in equation A.

Solving for

Subtracting both sides by

Dividing both sides by 10.

∴

Thus, in 4 months Plan A will cost the same as Plan B

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.