Arental car company offers two rental plans, plan a and plan b, for the same economy size car. for both plans, the total rental cost, ƒ(m ) is a function of the number of miles, m, that the car is driven. plan a: ƒ(m ) = 0.12m + 75 plan b: ƒ(m ) = 0.35m i. in complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven. ii. for each function, determine how the rate of change will affect the total cost of a car rental. iii. for a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective.

Ithe verbal model describing the above situation will be: a rental company that offers two rental plans, plan a and plan b, for the same economy size car. for both pans the total cost is given by, f(m) which is a function of the number of miles,m, that the car has been driven. plan a charges flat fee of $75  and an additional rate for an unlimited number of miles of 0.12 per mile. plan b has an offer of $ 0.35 per mile but with no flat fee charges for rental.ii. the rate of change for plan a will increase the the cost per mile by a factor of $0.12 while in plan b the rate of change will increase the cost per mile by a factor of $3.5.iii] if m=250 miles: the cost of plan a will be: f(250)=0.12×250+75=$105the cost of plan b will be: f(250)=0.35×250=$87.5comparing the cost of both plans, plan b is the most cost effective.

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