Question

Who can help with piecewise functions?

Question is about electricity rates charges.
Base charge is $7.00
First 400kWh or less at 0.0450/kWh
Over 400 kWh at 0.0750/kWh

I know that w(x)=7.00+0.0450x if 400 or less kWh
I am confused how to write out the solution for over 400kWh.
The solution is telling me it is: -5+0.0750x but where did the -5 come from?

Answer 1

use w(x)=7.00+0.0450x to find the value of w(x) when x = 400

what do you get?

Answer 2

Yes I understand how to form the functions for up to 400 kWh but it's the over 400 kWh part that is tricking me out

Answer 3

I figured it out!
the solution to 7.00+0.045x when x is 400 is 25.
Then we would add the 25 to the next values
=25+0.075(x-400) ..... then distribute whats outside the parenthesis to whats inside
=25+0.075x-30...... then combine like terms(in this case just adding 25+ -30 to get -5
=-5+0.075x
Yay

Answer 4

Or you can think of it like this

some linear function y = mx+b goes through (400,25). We know the slope for that piece is 0.075, so m = 0.075

plug in m = 0.075, x = 400, y = 25. Then solve for b



y = mx+b
25 = 0.075*400+b
25 = 30+b
25-30 = 30+b-30
-5 = b
b = -5


So y = mx+b turns into y = 0.075x-5 which is the same as y = -5+0.075x

Answer 5

Oh man amazing. That is a great way to find it also, I am going to write this down for the future problems. Thank you!!!!

Answer 6

you're welcome