Question 601·Medium·Math

0 / 2000

A cell-phone company models a customer’s monthly bill with the function

C(n)=25n+40,

where $C(n)$ is the total charge, in dollars, for using $n$ gigabytes of data beyond the monthly allowance.
If Ashley’s bill last month was $165, how many gigabytes beyond the allowance did she use?

A linear function with a fixed fee and a per-unit charge gives a total from the number of units used. When the total is known but the usage is missing, set the function equal to that total and use a Desmos regression to find the input. The known bill is the output, not the input. Keep the fixed fee in the equation.

Hints

Hint 1
A function's output is the number its rule gives for an input. Here $C(n)$ is in dollars and $n$ is in gigabytes, so which one should equal Ashley's known bill?
Hint 2
A regression finds a missing value that makes two sides match. Define $C(x)$ from the bill rule, then enter $C(x_1)\sim165$ . The $\sim$ asks Desmos to find the missing input $x_1$ .

Step-by-step

Match the bill to the function's output
Step 1
Turn the bill into an equation
In the rule, the $40$ is charged even when $n=0$ , and the $25n$ charges $25$ for each extra gigabyte. Ashley's $165 bill is the output $C(n)$ , not the input $n$ , so match the rule to her bill: $C(n)=165\quad\text{so}\quad25n+40=165$ .
Step 2
Find the missing gigabytes in Desmos
Type $C(x)=25x+40$ , then $C(x_1)\sim165$ . Here $x_1$ stands for the unknown input, and a regression uses $\sim$ to find the value that makes the bill equal $165$ . Under PARAMETERS, Desmos shows $x_1=5$ , so Ashley used $5$ gigabytes beyond her allowance. Choice C.

Question 601·Medium·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this