Question

which equation represents exponential decay? a. $y = \frac{1}{100}(31)^x$ b. $y = \frac{1}{10}(3.1)^x$ c. $y = 10(0.13)^x$ d. $y = 100(1.03)^x$

Explanation:

Step1: Recall Exponential Decay Form

The general form of an exponential decay function is \( y = a(b)^x \), where \( 0 < b < 1 \), and \( a>0 \).

Step2: Analyze Each Option

• Option A: \( y=\frac{1}{100}(31)^x \). Here, \( b = 31>1 \), so this is exponential growth, not decay.
• Option B: \( y=\frac{1}{10}(3.1)^x \). Here, \( b = 3.1>1 \), so this is exponential growth, not decay.
• Option C: \( y = 10(0.13)^x \). Here, \( a = 10>0 \) and \( 0<0.13<1 \), which fits the exponential decay form.
• Option D: \( y = 100(1.03)^x \). Here, \( b = 1.03>1 \), so this is exponential growth, not decay.

Answer:

C. \( y = 10(0.13)^x \)