Question

1. which value of b would most likely represent exponential decay in the function $f(x) = ab^x$?

a. $b = 0.3$
b. $b = 2$
c. $b = 1$
d. $b = 5$

Explanation:

Step1: Recall exponential decay condition

For the exponential function \( f(x) = ab^x \), exponential decay occurs when \( 0 < b < 1 \).

Step2: Analyze each option

• Option a: \( b = 0.3 \), and \( 0 < 0.3 < 1 \), so this satisfies the decay condition.
• Option b: \( b = 2 \), \( 2>1 \), this is exponential growth.
• Option c: \( b = 1 \), \( f(x)=a(1)^x=a \), this is a constant function, not decay.
• Option d: \( b = 5 \), \( 5>1 \), this is exponential growth.

Answer:

a. \( b = 0.3 \)