Answer:
To the nearest percentage, percent increase is 33%
Step-by-step explanation:
Mathematically;
Percentage increase = (new - old)/old * 100%
new = 48 hours
old = 36 hours
% increase = (48-36)/36 * 100%
12/36 * 100%
1/3 * 100%
= 33.33%
1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation
Remember yo can do anything to an equation as long as you do it to both sides
so
remember distributive property
a(b+c)=ab+ac
so first distribute
2(3x)+2(-9)=18x
6x-18=18x
minus 6x both sides
-18=12x
divide both sides by 12
-18/12=x
-9/6=x
-3/2=x
easier way is to first divide both sides by 2
x=-3/2
