Final answer:
The exponential decay function is represented by f(x) = Four-fifths (five-fourths)^x.
The answer is option ⇒1
Step-by-step explanation:
The exponential decay function f(x) = Four-fifths (five-fourths)^x represents a decay process where the value of the function decreases as x increases.
Let's break down the function step-by-step:
1. The base of the exponential function is (five-fourths). This means that the value of (five-fourths)^x is repeatedly multiplied by itself as x increases.
2. The coefficient of the exponential function is Four-fifths. This means that the value of the exponential function is multiplied by Four-fifths.
3. The overall effect of the function is decay. As x increases, the value of the exponential term (five-fourths)^x decreases, and then it is multiplied by Four-fifths, further decreasing the value.
For example, let's evaluate the function at x = 1:
f(1) = Four-fifths (five-fourths)^1
Calculating (five-fourths)^1 gives us (5/4)^1 = 5/4.
Multiplying (5/4) by Four-fifths gives us (4/5) * (5/4) = 1.
So, f(1) = 1.
This means that when x = 1, the function has a value of 1.
In general, as x increases, the value of the function f(x) will decrease due to the exponential decay behavior of the function.
The answer is option ⇒1