Respuesta :
Answer:
its g(x) is exponential; an exponential function increases faster than a linear function. I got it right.
Step-by-step explanation:
There are several functions that can be used to model different situations.
g(x) represents an exponential function
An exponential function is represented as:
[tex]\mathbf{y = ab^x}[/tex]
For g(x)
Represent the years from 1995 with x.
- When year = 1995, x =0 and y = 72429.27
- When year = 2000, x =5 and y = 79967.77
So, we have:
[tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{ab^0 = 72429.27}[/tex]
[tex]\mathbf{a = 72429.27}[/tex]
[tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{ab^5 = 79967.77}[/tex]
Substitute [tex]\mathbf{a = 72429.27}[/tex]
[tex]\mathbf{72429.27b^5 = 79967.77}[/tex]
Divide both sides by 72429.27
[tex]\mathbf{b^5 = 1.1041}[/tex]
Take 5th root of both sides
[tex]\mathbf{b = 1.02}[/tex]
So, the function is:
[tex]\mathbf{g(x) = 72429.27(1.02)^x}[/tex]
In 2005, when x = 10, we have:
[tex]\mathbf{g(10) = 72429.27(1.02)^{10} = 88290.88}[/tex]
In 2006, when x = 11, we have:
[tex]\mathbf{g(10) = 72429.27(1.02)^{11} = 90056.70}[/tex]
And so on.
Hence, g(x) is exponential; an exponential function increases faster than a linear function.
Read more about exponential functions at:
https://brainly.com/question/13545998
