SOLUTION: The cost of maintenance on an automobile increases each year by 10% and Andrew paid $300 this year for maintenance on his automobile. If the cost c for maintenance on Andrew’s auto
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Question 341341: The cost of maintenance on an automobile increases each year by 10% and Andrew paid $300 this year for maintenance on his automobile. If the cost c for maintenance on Andrew’s automobile n years from now is given by the function
c(n) = 300x^n , what is the value of x?
A. 0.1 B. 0.3 C. 1.1 D. 1.3 E. 30 Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! cost this year is 300.
annual growth rate percentage is 10%.
formula is c(n) = 300*x^n
x is equal to 10% divided by 100% + 1 which makes x = 1.10
your formula becomes c(n) = 300*(1.10)^n.
in 5 years time, the maintenance will be equal to 300 * (1.10)^5 = 483.153.
in 10 years time, the maintenance will be equal to 300 * (1.10)^10 = 778.122738
you would graph this equation on a horizontal axis of x and a vertical axis of y as follows:
allow c(n) to be equal to y.
allow n to be equal to x.
your equation becomes:
y = 300*(1.10)^x
graph of this equation would look as follows:
horizontal lines were drawn at y = 300 and y = 483.l153 and y = 778.122738.
drop a vertical line from the intersection of those horizontal lines with the graph of the equation and you will see that they intersect where x = 0 (y = 300) and x = 5 (y = 483.153) and x = 10 (y = 778.122738).
you should also see that the name of the variable is important to its application at the time that it is being used only.
we started with c(n) = x^n
we calculated x to be equal to 1.1
our equation became c(n) = 1.10^n
the variable x is not important to the equation anymore as it has been replaced with the value of 1.10.
we then assigned the variable c(n) to be equal to y.
we then assigned the variable n to be equal to x.
this allows us to replace those variables in the equation to get:
y = 1.10^x
the variable x has taken the place of the variable n in representing the exponent in the equation.
the variable y has taken the place of the variable c(n) in representing the result of the calculation of the equation.
the equation remains the same.
only the names of the variables has changed.
this was done to allow the graphing to take place because the graphing software only recognizes the variables of x and y .
your original answer of x = 1.10 is still valid.
the rest was just added to show you how this looked on a graph.
your answer is selection C.
