QuestionWhich of the contexts below could not be modeled by a linear function?
Answer
A town's population grows at a
An elevator descends at a rate rate of every year. of 24 feet per second.
Latanya puts \\ of data used.
Studdy Solution
STEP 1
What is this asking?
Which of these situations doesn't involve something changing at a constant rate?
Watch out!
Percentage growth can be tricky!
It might seem linear, but it's not!
STEP 2
1. Analyze Population Growth
2. Analyze Elevator Descent
3. Analyze Savings Account
4. Analyze Data Plan
STEP 3
Let's imagine a town starts with 100 people.
A 4.5% growth means the town adds people the first year.
So, after one year, the population is people.
STEP 4
The *next* year, the growth is people.
Notice how the *amount* of growth changed!
It's not the same amount each year, even though the *percentage* is the same.
This is a tell-tale sign of non-linear growth!
STEP 5
The elevator descends at a constant rate of feet per second.
This means every second, the elevator's height decreases by the same amount: feet.
Constant change?
Sounds linear to me!
STEP 6
Latanya adds to her savings account every month.
This is a constant increase!
If she starts with , after one month she has .
After two months, she has , and so on.
This is definitely linear!
STEP 7
The data plan has a fixed cost of per month, plus a variable cost of per GB.
The total cost increases at a constant rate for each GB used.
So, this situation can be modeled by a linear function!
STEP 8
The town's population growth is not linear.
The population increases by a *percentage* each year, not a fixed amount.
This means the growth is not constant, so it can't be modeled by a linear function.
The other situations (elevator descent, savings, and data plan) all involve constant changes, making them linear.
So the answer is the town's population growth.
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