Answer:
For [tex]P = 1[/tex] ; [tex]a = 10[/tex], the function [tex]f(x) = Pa^{x}[/tex] would become [tex]f(x) = 10^{x}[/tex] which is an exponential growth function. So, option D is correct.
Please check the attached figure a for visualizing the graph of [tex]f(x) = 10^{x}[/tex].
Step-by-step explanation:
As the function is given by
[tex]f(x) = Pa^{x}[/tex]
For a function to be an exponential growth function
For a function to be an exponential decay function
For a function to have no change
If we carefully observe the choices, it is easy to determine that putting [tex]P = 1[/tex] ; [tex]a = 10[/tex] in [tex]f(x) = Pa^{x}[/tex] would bring [tex]f(x) = 10^{x}[/tex].
So, [tex]f(x) = 10^{x}[/tex] would be an exponential growth function. The graph of [tex]f(x) = 10^{x}[/tex] is shown in figure a.
So, out of all the available options, only option D is correct i.e. [tex]P = 1[/tex] ; [tex]a = 10[/tex].
Keywords: exponential growth function, exponential decay function
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