Membership warehouse clubs offer shoppers low​ prices, along with rewards of cash back on club purchases. If the yearly fee for a warehouse club membership is​ $100 and the reward rate is 2​% on club purchases for the​ year, then the linear equation y=100−0.02x models the actual yearly cost of the membership​ y, in dollars. Here x represents the yearly amount of club​ purchases, also in dollars.
​a) Determine the actual yearly cost of the membership if club purchases for the year
are ​$1500.
​b) What amount of club purchases would reduce the actual yearly cost of the membership
to ​$47​?
​c) How much would a member have to spend in yearly club purchases to reduce the
yearly membership cost to​ $0?
a) The actual yearly cost of the membership if club purchases for the year are ​$1500 is ​$___.
​(Simplify your answer. Type an integer or a​ decimal.)