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The function
f is defined by
f(x)=450(0.3)^(x). If
f(a)=450, what is the value of
a ?

The function $f$ is defined by $f(x)=450(0.3)^{x}$ . If $f(a)=450$ , what is the value of $a$ ?

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Evaluate expression when two complex numbers are given

Full solution

Q. The function

f

is defined by

f(x)=450(0.3)^{x}

. If

f(a)=450

, what is the value of

a

?

Given Function and Condition: We are given the function $f(x) = 450(0.3)^x$ and the condition $f(a) = 450$ . We need to find the value of $a$ .
Set Function Equal and Solve: Set the function equal to $450$ and solve for $a$ . $\newline$ $450 = 450(0.3)^a$
Isolate Exponential Term: Divide both sides of the equation by $450$ to isolate the exponential term. $\newline$ $\frac{450}{450} = \frac{450(0.3)^a}{450}$ $\newline$ $1 = (0.3)^a$
Recognize Exponential Property: Recognize that any non-zero number raised to the power of $0$ is $1$ . $(0.3)^0 = 1$
Final Value of a: Since $(0.3)^a = 1$ , and we know that $(0.3)^0 = 1$ , it follows that $a$ must be $0$ . $\newline$ $a = 0$

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