Given:
The exponential function is:
[tex]y=190(1.471)^x[/tex]
To find:
The percentage of increase or decrease.
Solution:
The general exponential function is:
[tex]y=a(1+r)^x[/tex] ...(i)
Where, a is the initial value,t is the time period, r is the rate of increase if [tex]r>0[/tex] and r is the rate of decrease if [tex]r<0[/tex].
We have,
[tex]y=190(1.471)^x[/tex]
It can be written as:
[tex]y=190(1+0.471)^x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=0.471[/tex]
Since [tex]r>0[/tex], therefore the given function is an increasing function.
[tex]r\%=0.471\times 100[/tex]
[tex]r\%=47.1\%[/tex]
Therefore, the percentage of increase is 47.1%.
