Let's analyze each situation to determine whether it is better modeled by a linear function or an exponential function:
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Joe's savings increase by 10% every year.
This situation describes a percentage increase, which means his savings grow by a specific proportion relative to their current value. This is characteristic of exponential growth.
Model: Exponential. -
The number of people who do not have a smartphone is decreasing by 1/8 each year.
This situation also involves a proportionate decrease, indicating that the decline in the number of people is dependent on the current number. This is also characteristic of exponential decay.
Model: Exponential. -
Chad makes $15 per hour at his summer job.
Here, Chad's earnings increase in a fixed amount for each hour he works, meaning his total earnings can be calculated by multiplying the number of hours worked by the hourly wage. This is a linear relationship.
Model: Linear. -
Each cup of pancake mix makes exactly 6 pancakes.
This situation can be represented by a linear relationship where the number of pancakes made is directly proportional to the number of cups of pancake mix used. If you use more cups, you get more pancakes in a fixed ratio of 6 pancakes per cup.
Model: Linear.
To summarize:
- Joe's savings: Exponential
- People without a smartphone: Exponential
- Chad's earnings: Linear
- Pancakes from mix: Linear
1 answer