Answer:
Step-by-step explanation:
Note that the cost function is [tex]c(x) = 7.1+23\ln(x) [/tex], which gives us the cost of electricity for x hours of consumption
a). The function [tex]c^{-1}(x)[tex] which is the inverse function, tells us given a cost, the amount of hours we can consume electricty.
b) Consider the equation
[tex]y=7.1+23\ln(x)[/tex]
To find out the inverse function, we interchange the labels of x and y and solve for y, that is
[tex] x = 7.1+23\ln(y)[/tex]
when solved for y we have
[tex] e^{\frac{x-7.1}{23}}= y [/tex]
So the inverse function is given by [tex]c^{-1}(x) = e^{\frac{x-7.1}{23}}[/tex].
c) We will use the inverse function to find the amount of hours the customer can use eelectricity. It is simple obtained by evaluating the inverse function at the desired cost (i.e [tex]c^{-1}(15)[/tex])
that is
[tex]e^{\frac{15-7.1}{23}} = 1.409[/tex]
that is, the custome can consume at most 1.41 hours of electricity.
Answer:
Please read the answer below
Step-by-step explanation:
We have the function
[tex]y(x)=7.1+23logx[/tex]
A. With c^{-1}(x) we can calculate the hours of electricity for a definite cost
B.
c^{-1} can be calculated by taking into account that:
[tex]c^{-1}(x)=\frac{1}{c(x)}=\frac{1}{7.1+23logx}[/tex]
the denominator must be different of zero, hence we have for x:
[tex]7.1+23logx=0\\\\7.1+logx^{23}=0\\\\logx^{23}=-7.1\\\\10^{logx^{23}}=10^{-7.1}\\\\x^23=10^{-7.1}\\\\x=10^{\frac{-7.1}{23}}=0.49\approx0.5[/tex]
x must be different of 0.48
C.
By taking apart the function c(x) we have:
[tex]logx^{23}=15-7.1=7.9\\\\10^{logx^{23}}=10^{7.9}\\\\x=10^{\frac{7.9}{23}}=2.2h[/tex]
x=2.2h
hope this helps!
