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interpret the practical meaning of the derivative

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40) The value of a certain automobile purchased in 1997 can be approximated by the function v(t)=25(0.85)^t , where t is the time in years, from the date of purchase, and v is the value, in thousands of dollars.
(a) Evaluate and interpret v(4).
(b) Find an expression for v1(t) including units.
(c) Evaluate and interpret v1(4).
(d) Use v(t), v1(t) and any other considerations you think are relevant to write a paragraph in support of or in opposition to the following statement: From a momentary point of view, it is best to keep this vehicle as long as possible".

56) Let f(v) be the gas consumption ( in liters/km ) of a car going at velocity v( in km/hr). In other words , f(v) tells you how many liters of gas the car uses to go one kilometer , if it is going at a velocity v, you are told that
f(80)=0.05 and f1(80)=0.0005.

a) Let g(v) be the distance the same car goes on one liter of gas at velocity v. what is the relationship between f(v) and g(v) ? find g(80) and g1(80).
b) Let h(v) be the gas consumption in liters per hour. In other words, h(v) tells you how many liters of gas the car uses in one hour if it is going at velocity v. what is the relationship between h(v) and f(v)?
Find h(80) and h1(80).
c) How would you explain the practical meaning of the values of these functions and their derivatives to a driver who knows no calculus?

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The solution evaluates the functions and calculates and interprets the meaning of its derivative in the contexts.

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