credit/debit cards: annual transactions on master card debit cards that do noyre
ID: 3095110 • Letter: C
Question
credit/debit cards: annual transactions on master card debit cards that do noyrequire a pin code have grown from about 10 billion in 1997 to110 billion in 2002 a)find the linear function given by : T(x) =m(x-x1)+y1 that models thesedata,where x is the year b)Use T(x) tp estimate years when the annualtransactions were between 50 billion and 90billion. thanks credit/debit cards: annual transactions on master card debit cards that do noyrequire a pin code have grown from about 10 billion in 1997 to110 billion in 2002 a)find the linear function given by : T(x) =m(x-x1)+y1 that models thesedata,where x is the year b)Use T(x) tp estimate years when the annualtransactions were between 50 billion and 90billion. thanks thanksExplanation / Answer
Since x represents the year, we can label the data as pointswhere the x-value is the year and the transactions are the y. Sothat gives us two points: (We'll use x-values that are years since1997, so 1997 = 0 and 2002 = 5). (0, 10) and (5, 110) but remember that the y values areactually in billions of dollars. Now use these two points to calculate a slope: m = (110 - 10)/(5-0) m = 20 T(x) = m(x-x1) + y1 so T(x) = 20(x-0) +10 (We use the m we calculated and eitherpoint to plug in to the T(x) form provided) T(x) = 20x +10 T(x) = 20x + 10 (This is answerfor part a) Part b) Now that we have the T(x) function, we just plug in 50and 90 in for T(x) and solve for x 50 = 20x + 10 40 = 20x x= 2 (But this is two years after 1997 sothe year is actually 1999) Now we do the same for 90 billion 90 = 20x + 10 80 = 20x x=4 (Again, this is 4 years after 1997 so itwould be 2001) So between the years 1999 and 2001 annual transactions werebetween 50 billion and 90 billion. So between the years 1999 and 2001 annual transactions werebetween 50 billion and 90 billion.Related Questions
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