Given:
The exponential function is
[tex]y=2200(1.074)^x[/tex]
To find:
The percentage rate of increase or decrease.
Solution:
The general form of an exponential function is
[tex]y=a(1+r)^x[/tex] ...(i)
Where, a is the initial value, r<0 is the rate of decrease, r>0 rate of increase, x is time period.
We have,
[tex]y=2200(1.074)^x[/tex]
It can be written as
[tex]y=2200(1+0.074)^x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=0.074[/tex]
r>0, so the it is the rate of increase. Multiply it by 100 to get the percentage rate of increase.
[tex]r=0.074\times 100\%[/tex]
[tex]r=7.4\%[/tex]
Therefore, the percentage rate of increase is 7.4%.