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Determine whether each situation would be better modeled by a linear function or an exponential function

Daycare for Nancy is taller cost 215$ per week
The value Franco’s car decreased by 8%annually
The number of downloads of the new mobile game doubles every month
Caleb pays $12 per month for music streaming service

1 answer

Let's analyze each situation to determine whether it would be better modeled by a linear function or an exponential function.

  1. Daycare for Nancy is a constant cost of $215 per week:

    • This situation involves a fixed amount being paid each week. Since the cost does not change but remains constant over time, it is best modeled by a linear function.

  2. The value of Franco’s car decreased by 8% annually:

    • This situation involves a percentage decrease relative to the current value of the car. As the value decreases, the amount it decreases will also be a percentage of a smaller and smaller amount each year. This is characteristic of exponential decay. Therefore, it is best modeled by an exponential function.

  3. The number of downloads of the new mobile game doubles every month:

    • Here, the number of downloads is increasing by a multiplicative factor (doubling) each month. This type of growth is characteristic of exponential functions, so it is best modeled by an exponential function.

  4. Caleb pays $12 per month for a music streaming service:

    • This situation involves a constant payment of $12 each month. Since the cost remains the same regardless of the number of months, it is best modeled by a linear function.

Summary:

  • Daycare for Nancy: Linear function
  • The value of Franco’s car: Exponential function
  • Number of downloads of the mobile game: Exponential function
  • Caleb's music streaming service: Linear function