A constant rate signals a linear function: the cost changes by the same amount each year. First translate the dates into years since the stated starting year. Then use Desmos to divide the change in cost by the elapsed years and find the slope. The later cost is not the starting value.
Hints
- Hint 1
The input means years after 2017, so 2017 is . How many years after 2017 is 2022? The cost at is the intercept, the fixed number in the function.
- Hint 2
The slope is the cost change per year, not the entire increase. Divide the difference between the two monthly costs by the number of years between the dates.
Step-by-step
Find the yearly rate and starting cost
Step 1Translate the dates into inputs
Because counts years after 2017, 2017 is and 2022 is . The cost change happened over five years, not one.
- Step 2
Find the increase per year
Use cost change divided by time change to find the slope, the change in monthly cost per year. Type in Desmos. It displays , so the monthly cost rose by $3.05 per year.
- Step 3
Identify the starting cost
The y-intercept is the cost when . That year is 2017, so . Using the 2022 cost here would put it at the wrong year.
- Step 4
Write the linear function
In slope-intercept form, : is the yearly increase and is the starting monthly cost. Use the rate and starting cost you found: . This models the average monthly cost, in dollars, years after 2017. Choice A.