In a linear model connecting a count to money, the number multiplied by the count is the rate per item. The number not multiplied by the count is the starting amount. Evaluate the model at an input of zero to check that amount, then interpret its sign in the story. Don’t mistake a negative starting amount for a loss on every item.
Hints
- Hint 1
A rate of change tells you how many dollars the revenue changes with each additional download. Which number is multiplied by the download count, and which number stays the same as that count changes?
- Hint 2
An intercept is where a graph crosses an axis. The starting revenue is the vertical-axis intercept, found at zero downloads. What does the model say about the label’s starting balance?
Step-by-step
Find the starting revenue
Step 1Separate the rate from the fixed amount
The rate of change is dollars per download because multiplies the download count . The is not multiplied by , so it isn’t a loss on every download.
- Step 2
Find the revenue at zero downloads
Set the input to zero to find the starting output. Here that means . Type , then in Desmos. It shows , so the model gives negative net revenue before any downloads.
- Step 3
Interpret the negative starting amount
Net revenue is money left after costs. Starting at dollars means the label has a $350 upfront cost to cover. According to the model, the label spent $350 before any downloads were made. Choice D.