Linear or exponential?
Definitions
- linearly, if it grows (decays) by a constant amount for each unit of time.
- exponentially, if it grows (decays) by a constant factor or rate for each unit of time.
Choosing a linear vs. an exponential model
When data are given in a table...
- the difference of the corresponding outputs is constant, then the data set in the table can be modeled by a linear function.
- the quotient of the corresponding outputs is constant, then the data set in the table can be modeled by an exponential function.
Linear or exponential?
The following equation represents the change over time of the quantity of goods that don't match the quality criteria of a factory, since it started business: Q(t)=1594(0.947)t
The following equation represents the cost in Euros of a dozen of eggs in Italy, since in year 2000. C(t)=2.02+0.11t
Decide whether the following table represents a linear or exponential function.
t 0 1 2 3 f(t) 2 1 0.5 0.25
Your investments account starts with $10. Every year, the amount of money in your account is tripled.
Bowling players must pay $15 for a membership card, plus $5 each time they play.
You have 96 tickets for a them park. The admission fee you have to pay for every attraction is 4 tickets.
Decide whether the following table represents a linear or exponential function.
t 0 1 2 3 f(t) 0.4 3.6 6.8 10
A student has 56 books, and adds to her collection 12 books each year.