The resale value V, in dollars, of a certain car is a function of the number of years t since the year 2012. In the year 2012 the resale value is $18,000, and each year thereafter the resale value decreases by $1700. (a) What is the resale value in the year 2013? $| (b) Find a formula for V as a function oft. V = (c) Make the graph of V versus t covering the first 4 years since the year 2012. V V 20000- 25 000 20 000 15 000- 15 000 10000 10 000 5000 5000 1 2 4 1 2 3 4 V V 20000 25 000 20 000- 15 000 15 000- 10000 10000 5000 5000 2 3 4 1 3 (d) Use functional notation to express the resale value in the year 2015. Calculate that value.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Resale value V of a car is a function of number of years 't' since the year 2012.
Given that the resale value of certain car in the year 2012 is $18,000.
And each year the resale value decreases by $1700.
(a) The resale value at the year 2012 = $18,000
Since each year the resale value decreases by $1700
∴ Resale value in the year 2013 = $18,000 - $1700 = $16,300
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