Question

1. f(x) = 3.5

11. f(x) = (4)
III. f(x) = -7e* + 8
Identify the functions which represent exponential decay?
A) I and II only
B) I and Ill only
C) 1.11, and III
D) II and III only

Answer 1

In identifying exponential decay functions, we look for a form that has a negative exponent in the term with the base e. Amongst the options given, only the third function f(x) = -7e^x + 8 represents exponential decay because it has a negative base multiplier indicating a decreasing rate of change. Therefore, the only function that represents an exponential decay is option III. The correct answer is B) I and III only.

Step-by-step explanation:

The question asks to identify which functions represent exponential decay. An exponential decay function is of the form f(x) = a · e(-kx), where a is a positive constant, e is the base of natural logarithms, and k is a positive constant that represents the decay rate. For a function to represent exponential decay, its rate of change must decrease as x increases, which typically involves a negative exponent in the term with the base e.

Looking at the given functions:

• f(x) = 3.5 does not have the form of an exponential function.
• f(x) = 4 is also not an exponential function because it is a constant function.
• f(x) = -7ex + 8 is an example of exponential decay because the term -7ex indicates a decay with a negative base multiplier in front of the e term.

Therefore, the only function that represents an exponential decay is option III. The correct answer is B) I and III only.