Guadalupe's credit card has an apr of 23%, calculated on the previous
monthly balance, and a minimum payment of 2%, starting the month after the
first purchase. her credit card record for the last 7 months is shown in the
table below.
end of
month
previous
balance
$0.00
$900.00
$899.25
5898.50
5897.75
5897.00
5896 26
new
charges
$900.00
$0.00
$0.00
50.00
$0.00
$0.00
50.00
payment
received
$0.00
$18.00
$17.99
$17.97
$17.96
$17.94
$17 93
finance
charges
$0.00
$17.25
$17.24
$17.22
$17 21
$17 19
$17 18
principal
paid
$0.00
$0.75
$0.75
50.75
$0.75
$0 75
50 75
new
balance
$900.00
$899.25
$898.50
$897.75
$897.00
$896 26
$895 51
vou
how is the new balance calculated?

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!