Question

assignment 6.1 exponential functions
due oct 28 by 11:59pm points 10 submitting an external tool
available until dec 12 at 11:59pm
assignment 6.1 exponential functions
score: 1/10 answered: 1/10
question 2
for the function $f(x) = 5^{-x}$ calculate the following function values.
enter your answer as a simplified fraction or integer.
$f(3) = $
$f(4) = $

Explanation:

Step1: Recall the exponent rule

Recall that \( a^{-n}=\frac{1}{a^{n}} \) for any non - zero real number \( a \) and positive integer \( n \). For the function \( f(x) = 5^{-x}\), we can rewrite it as \( f(x)=\frac{1}{5^{x}} \) using the negative exponent rule.

Step2: Calculate \( f(3) \)

To find \( f(3) \), we substitute \( x = 3 \) into the function \( f(x)=\frac{1}{5^{x}} \). So \( f(3)=\frac{1}{5^{3}} \). Since \( 5^{3}=5\times5\times5 = 125 \), then \( f(3)=\frac{1}{125} \).

Step3: Calculate \( f(4) \)

To find \( f(4) \), we substitute \( x = 4 \) into the function \( f(x)=\frac{1}{5^{x}} \). So \( f(4)=\frac{1}{5^{4}} \). Since \( 5^{4}=5\times5\times5\times5=625 \), then \( f(4)=\frac{1}{625} \).

Answer:

\( f(3)=\frac{1}{125} \), \( f(4)=\frac{1}{625} \)