The table below represents the amount of money in Sylvester’s bank account as a function of the number of years since he opened the account. Does this situation represent a linear or non-linear function, and why?Amount of Money in Sylvester’s Bank AccountYearsAmount of Money (dollars)150021,00041,50082,000162,500
Answer
I
It represents a linear function because there is a constant rate of change.
I
It represents a linear function because there is not a constant rate of change.
I
It represents a non-linear function because there is a constant rate of change.
I
It represents a non-linear function because there is not a constant rate of change.
Explanation
A function is linear when its rate of change is constant. From year 1 to year 2, the amount increases by $500 per year; from year 2 to year 4, it increases by $250 per year. These rates are different, so the function is non-linear because it does not have a constant rate of change.
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