Question

state whether the equation represents exponential growth, exponential decay, or neither.
$y = 2 \cdot 1.05^x$

choose the correct answer below.
\\(\circ\\) exponential decay
\\(\circ\\) exponential growth
\\(\circ\\) neither

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a \cdot b^x \), where \( a>0 \) and \( b>0 \). If \( b > 1 \), it's exponential growth; if \( 0 < b < 1 \), it's exponential decay.

Step2: Identify \( b \) in the given equation

In the equation \( y = 2 \cdot 1.05^x \), we have \( a = 2 \) and \( b = 1.05 \).

Step3: Compare \( b \) with 1

Since \( 1.05>1 \), by the definition of exponential growth (when \( b > 1 \) in \( y = a \cdot b^x \)), this function represents exponential growth.

Answer:

B. Exponential growth