The parameters of the exponential function are given as follows:
a = 3, b = 0.5, y-intercept (0, 3).
The numeric values are given as follows:
The end behavior is described as follows:
The graph is plotted at the end of the answer.
What is an exponential function?
An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
- a is the initial value, which is also the y-intercept.
For this problem, the function is given by:
[tex]f(x) = 3(0.5)^x[/tex]
Hence the parameters are:
a = 3, b = 0.5, y-intercept (0, 3).
The numeric values are given by:
- x = -2: [tex]f(-2) = 3(0.5)^{-2} = 3(2)^2 = 12[/tex].
- x = -1: [tex]f(-1) = 3(0.5)^{-1} = 3(2)^1 = 6[/tex].
- x = 0: [tex]f(0) = 3(0.5)^0 = 3[/tex].
- x = 1: [tex]f(1) = 3(0.5)^1 = 1.5[/tex].
- x = 2: [tex]f(2) = 3(0.5)^2 = 0.75[/tex].
The end behavior is the limits of f(x) as x goes to negative infinity and positive infinity, hence:
- [tex]\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} 3(0.5)^x = 3(0.5)^{-\infty} = 3(2)^{\infty} = \infty[/tex]
- [tex]\lim_{x \rightarrow \infty} f(x) = [tex]\lim_{x \rightarrow \infty} 3(0.5)^x = 3(0.5)^{\infty} = 0[/tex]
Hence:
More can be learned about exponential functions at https://brainly.com/question/24808124
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