Question

Xcel energy uses the equation c (x) =7.1+23logx to determine the cost of electricity for x hours. A. What would the function c^-1(x) allow you to calculate. B. Find c^-1(x). C. If a customer can afford $15 per month for electricity, how long can he or she have electricity turned on?

Answer 1

Answer:

Step-by-step explanation:

Note that the cost function is $c(x) = 7.1+23\ln(x)$, which gives us the cost of electricity for x hours of consumption

a). The function $c^{-1}(x)[tex] which is the inverse function, tells us given a cost, the amount of hours we can consume electricty. b) Consider the equation [tex]y=7.1+23\ln(x)$

To find out the inverse function, we interchange the labels of x and y and solve for y, that is

$x = 7.1+23\ln(y)$

when solved for y we have

$e^{\frac{x-7.1}{23}}= y$

So the inverse function is given by $c^{-1}(x) = e^{\frac{x-7.1}{23}}$.

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 $c^{-1}(15)$)

that is

$e^{\frac{15-7.1}{23}} = 1.409$

that is, the custome can consume at most 1.41 hours of electricity.

Answer 2

Answer:

Please read the answer below

Step-by-step explanation:

We have the function

$y(x)=7.1+23logx$

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:

$c^{-1}(x)=\frac{1}{c(x)}=\frac{1}{7.1+23logx}$

the denominator must be different of zero, hence we have for x:

$7.1+23logx=0\\\\7.1+logx^{23}=0\\\\logx^{23}=-7.1\\\\10^{logx^{23}}=10^{-7.1}\\\\x^23=10^{-7.1}\\\\x=10^{\frac{-7.1}{23}}=0.49\approx0.5$

x must be different of 0.48

C.

By taking apart the function c(x) we have:

$logx^{23}=15-7.1=7.9\\\\10^{logx^{23}}=10^{7.9}\\\\x=10^{\frac{7.9}{23}}=2.2h$

x=2.2h

hope this helps!