Question

select the best description of the following exponential equation.
$f(x) = 85(9.43)^x$
show your work here

growing by 843% with every unit of x. decaying by 943% with every unit of x.
growing by 943% with every unit of x. decaying by 843% with every unit of x.

Explanation:

Step1: Recall Exponential Growth/Decay Formula

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial amount, and \( b \) determines growth or decay. If \( b>1 \), it's growth; if \( 0 < b < 1 \), it's decay. The growth rate is \( (b - 1)\times100\% \).

Step2: Analyze the Given Function

For \( f(x)=85(9.43)^x \), \( b = 9.43 \). Since \( 9.43>1 \), it's a growth function.

Step3: Calculate the Growth Rate

Growth rate \( = (9.43 - 1)\times100\% = 8.43\times100\% = 843\% \). So the function grows by 843% per unit of \( x \).

Answer:

Growing by 843% with every unit of \( x \) (the corresponding option, e.g., if the first option is "Growing by 843% with every unit of \( x \)", then the answer is that option).