A linear function changes by the same amount for each one-unit step in its input. For a population model, compare its Desmos outputs one day apart to find the daily change. Then check the units: the model may count in thousands even when the question asks for individual microorganisms. Convert both the population unit and the time unit.
Hints
- Hint 1
The rate of change is how much a model’s output changes when its input increases by one. Compare with to find the change over one day. What does a negative result tell you?
- Hint 2
Each unit of represents one thousand microorganisms, not one microorganism. After finding the size of the daily decrease, multiply it by to express it as a count of microorganisms.
- Hint 3
A unit rate tells you the change for one unit of time. Your count is for a day, but the question asks per hour. How many hours share that one day’s decrease?
Step-by-step
Compare two days in Desmos
Step 1Find the change over one day
A linear function has the same change over every one-day interval. Type in Desmos, then type . Desmos shows . The inputs are one day apart, so the negative sign means a decrease of thousand microorganisms per day.
- Step 2
Change thousands to individual microorganisms
Because is measured in thousands, multiply the size of the decrease by . Type ; Desmos shows . That’s microorganisms per day, not per hour.
- Step 3
Find the decrease per hour
There are hours in a day, so divide the daily decrease by . Type ; Desmos shows . The model estimates a decrease of microorganisms per hour. Choice A.