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Andre received $60 for his birthday and put it in his piggy bank. Each week, he puts 3 more dollars in his bank. The amount of money in dollars D in his bank is given by
D = 3w + 60 where w is the number of weeks he has saved 3 dollars. His sister Lana helped him find how much money he will have after 4, 15, 20, and 36 weeks. This table shows her results. What is the rate of change using Lana’s values for D and w? Is this a linear model or non-linear model?
W 4 weeks 15 weeks 20 weeks 36 weeks
D D= 3w =60 D = 3w + 60 D = 3w + 60 D = 3w + 60
= 3*4 +60 = 3 * 15 = 3 * 20 + 60 = 3 * 36 + 60
= 12 + 60 = 45 + 60 = 60 + 60 = 108 + 60
= 72 = 105 = 120 = 168
A.
The rate of change varies. It is a linear model.
B.
The rate of change varies. It is a non-linear model.
The answer is D. The rate of change is 3. It is a linear model.
The original equation D = 3w + 60 is in the form y = mx + b, in which m is always the rate of change. In this case, m = 3, so the rate of change is 3.
Also, when the rate of change is constant, the equation is always linear. If the equation was plotted on a coordinate plane, it would create a straight line.
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