Problema Solution
The function f(x) represents the total bill from a rental store that charges $10 to rent a power tool plus an additional $2 an hour. A second rental store uses the function g(x)=15 + 1.5x to represent the total bill for a similar power tool. Write both functions. Compare the rate of change and y intercepts of these two functions.
Answer provided by our tutors
First function
f(x) = 10 + 2x
Second function
g(x)=15 + 1.5x
The rate of change of these functions are simply their SLOPE and this can be seen simply by writing the equations in their standard form (y=mx+b). For the first function it is 2 and the second function is 1.5.
f(x) = 2x + 10
Rate of change: 2
g(x)= 1.5x + 15
Rate of change: 1.5
This means one store charges only $10 initially but becomes more expensive the longer you rent, the only store charges $15 initially but for a longer rental they would be cheaper.
Solving for the point of intersection by elimination (replacing "f(x)" with "y" for convenience:
y = 10 + 2x
y =15 + 1.5x
10+2x = 15 + 1.5x
15 - 10 = 2x - 1.5x
5=.5x
x=5/.5 = 10
using the first equation and x=10 to calculate y:
y=10+2(10)=30
checking the answer with the first equation:
y = 15 + 1.5(10) = 15 + 15 = 30
The point of intersection (10, 30) indicates that after 10 hours a rental the second store would be cheaper and at 10 hours both stores would charge $30.