Respuesta :
Given the exponential function:
[tex]y=590(1.061)^x[/tex]Let's determine if the exponential function represents growth or decay.
Take the exponential function:
[tex]y=a(b)^x[/tex]Where b is the base.
• If the base of an exponential function is greater than one, the exponential function represents growth
• If the base of an exponential function is between 0 and 1, the function represents a decay function.
Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.
SInce it is represents a growth function, let's determine the percentage rate of increase.
The general formula for exponential growth is:
[tex]y=a(1+r)^x[/tex]Where r is the growth rate.
Thus, we have:
[tex]\begin{gathered} y=590(1+(1-1.061)^x \\ \\ y=590(1+0.061)^x \end{gathered}[/tex]The growth rate, r is = 0.061
The percentage rate of increase is:
[tex]\text{percentage rate of increase = }0.061\ast100=6.1\text{\%}[/tex]Therefore, the percentage rate of increase is 6.1%
ANSWER:
The function represents growth
Percentage rate of increase = 6.1%
