Question

select the best description of the following exponential equation.
$f(x) = 76(0.99)^x$
show your work here

decaying by 1% with every unit of $x$.
decaying by 99% with every unit of $x$.
growing by 1% with every unit of $x$.
growing by 99% with every unit of $x$

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial amount, and \( b \) is the base. If \( 0 < b < 1 \), it's a decay function. The decay rate \( r \) is related to \( b \) by \( b = 1 - r \).

Step2: Analyze the given function

For \( f(x) = 76(0.99)^x \), the base \( b = 0.99 \). Since \( 0.99 < 1 \), it's a decay function. Now, find the decay rate: \( 1 - r = 0.99 \), so \( r = 1 - 0.99 = 0.01 = 1\% \). This means the function decays by 1% for each unit of \( x \).

Answer:

Decaying by 1% with every unit of \( x \)