Question

Andre received $60 for his birthday that he put in his piggy bank. Each week, he puts 3 more dollars in his bank so that the amount of money in dollars D in his bank is given by D = 3w + 60 where w is the number of weeks. His sister Lana helped him find how much money he will have after 4, 15, 20, and 36 weeks. The table below shows her results. Find the rate of change using Lana’s values for D and w. Explain whether this is a linear model.

Answer 1

after 4 weeks = 3(4) + 60 = 12 + 60 = 72
after 15 weeks = 3 (15) + 60 = 45 + 60 = 105
after 20 weeks = 3(20) + 60 = 60 + 60 =120
after 36 weeks = 3(36) + 60 = 108 + 60 =168
it is a linear model because it follows the form y = mx + c where m = 3 & c = 60.
the rate of change is equivalent to the slope (m) = 3