Question

select the best description of the following exponential equation.
$f(x) = 97(6.04)^x$
show your work here
hint: to add an exponent ($x^n$), type \exponent\ or press \^\
options:

• decaying by 604% with every unit of $x$.
• growing by 604% with every unit of $x$.
• growing by 504% with every unit of $x$.
• decaying by 504% with every unit of $x$

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth function is \( f(x) = a(b)^x \), where \( a>0 \) and \( b > 1 \). The growth rate \( r \) is related to \( b \) by \( b=1 + r \) (in decimal form) or \( b = 1+\frac{r}{100}\) (in percentage form).

Step2: Analyze the given function

For the function \( f(x)=97(6.04)^x \), we have \( b = 6.04 \). Since \( b>1 \), this is a growth function.

Step3: Calculate the growth rate

Using \( b=1 + r \) (where \( r \) is the growth rate in decimal), we solve for \( r \):
\( 6.04=1 + r \)
Subtract 1 from both sides: \( r=6.04 - 1=5.04 \)
To convert \( r \) to a percentage, multiply by 100: \( r = 5.04\times100\%=504\% \)

Answer:

Growing by 504% with every unit of \( x \) (the option: Growing by 504% with every unit of \( x \))