Question

I. ƒ(x) = 3 · x II. ƒ(x) = III. ƒ(x) = -7 8 Identify the functions which represent exponential decay. Responses AI and II onlyI and II only BI and III onlyI and III only CI, II, and IIII, II, and III DII and III only

Answer 1

None of the provided functions I, II, or III represent exponential decay; only function II is an exponential function but it signifies growth.

Step-by-step explanation:

An exponential decay function has the general form f(x) = a · b^x, where a is a positive constant, b is a positive constant less than 1, and x is the exponent. Given the functions
I. f(x) = 3 · x
II. f(x) = ⅛
III. f(x) = -7,
none of these are exponential functions. Therefore, the answer to the question is that none of the given functions represent exponential decay. Functions I and III are not even exponentials to begin with; function I is linear and III is a constant function. Function II is an exponential function, however, it represents exponential growth since the base of the exponential is greater than 1.

In summary, none of the functions I, II, or III represent exponential decay. Function II is an exponential, but it is of growth type since the base (⅛ or ¼ translated from the original Roman numeral II) is greater than 1, which signifies growth rather than decay.