For linear cost functions on the SAT, rewrite or recognize them in the form . The constant term is the fixed starting amount, and the coefficient of the variable counting items (like pages, hours, or miles) is the per-unit cost or rate—this coefficient is usually the answer they want, so identify it directly to save time.
Hints
- Hint 1
Think about fixed cost vs. per-page cost
If you print 0 pages, what does equal? That amount is the fixed fee, not the per-page cost.
- Hint 2
Look at how the cost changes with pages
Compare and . How much more do you pay when you go from 0 pages to 1 page? That increase is the cost of one page.
- Hint 3
Focus on the coefficient of
In a linear function like , the coefficient is the rate per unit (here, per page). Identify that coefficient in .
Desmos guide
- Step 1
Use a table to see the per-page cost
Type
C(p) = 18 + 0.12pinto Desmos, then use the table feature (tap the gear icon and select "Table"). Look at the values of when increases from 0 to 1; the amount that the total cost increases by is the cost of one page.
Step-by-step
- Step 1
Interpret the structure of the cost function
The function is , where is the total cost in dollars and is the number of pages. This has the form .
- Step 2
Identify the fixed fee and the per-page part
The term 18 does not depend on , so it is the fixed fee you pay even if you print 0 pages. The term changes when changes, so it represents the part of the cost that depends on how many pages you print.
- Step 3
Connect the coefficient of to the cost per page
The cost for each page is the amount added to the total cost for every increase of 1 in , which is exactly the coefficient of in the expression . Therefore, the cost of printing each individual page is dollars.