Question

number ten
y = 1.5^x
does the function represent growth or decay?
growth
what is the initial amount?

what is the rate of growth or decay?

Explanation:

Step1: Determine Growth/Decay

The general form of an exponential function is \( y = a b^x \), 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. Here, \( b = 1.5>1 \), so it's growth.

Step2: Find Initial Amount

In \( y = a b^x \), when \( x = 0 \), \( y=a b^0=a(1)=a \). For \( y = 1.5^x \), \( a = 1 \) (since it's \( y = 1\times1.5^x \)), so initial amount is \( 1 \).

Step3: Find Growth Rate

The growth rate is \( b - 1 \) for \( y = a b^x \) (when \( b>1 \)). Here, \( b = 1.5 \), so growth rate is \( 1.5 - 1=0.5 \) or \( 50\% \).

Answer:

• Does the function represent growth or decay? Growth
• What is the initial amount? 1
• What is the rate of growth or decay? 50% (or 0.5)