Answer:
Information
General form of an exponential function: [tex]y=ab^x[/tex]
where:
- [tex]a[/tex] is the y-intercept (or initial value)
- [tex]b[/tex] is the base (or growth factor)
- [tex]x[/tex] is the independent variable
Also, growth rate [tex]r=b-1[/tex]
Domain: input values - independent variable ⇒ [tex]x[/tex]
Range: output values - dependent variable ⇒ [tex]y[/tex]
y-intercept: when [tex]x=0[/tex]
Asymptote: the line(s) that the curve approaches as it tends towards infinity
Given function: [tex]f(x)=200(1.08)^x[/tex]
Solution
Domain: [tex]-\infty < x < +\infty[/tex]
Range: [tex]y > 0[/tex]
y-intercept ([tex]a[/tex]): [tex](0, 200)[/tex]
Asymptote: [tex]y=0[/tex]
Growth Rate ([tex]b-1[/tex]): [tex]0.08[/tex]
Growth Factor ([tex]b[/tex]): [tex]1.08[/tex]
End behaviors:
[tex]\textsf{as } x \rightarrow -\infty, f(x) \rightarrow0[/tex]
[tex]\textsf{as } x \rightarrow +\infty, f(x) \rightarrow+\infty[/tex]
