Question

Which function represents exponential decay?

f(x) =1/2 (3/2)^x

  f(x) =1/2 (-3/2)^x

  f(x) =4 (-2/3)^x

f(x) = 4 (2/3)^x

Answer 1

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay. So the function represents a exponential decay is f(x) = 4 (2/3)^x

Answer 2

For this case we have a function of the form:

`y = A * (b) ^ x`
Where,
A: initial amount
b: change of rate
b> 1: the exponential function grows
b <1: the exponential function decreases
x: independent variable
y: dependent variable
We then have the following function:

`f (x) = 4 (2/3) ^ x`
Where,

`b = 2/3`
As b <1 then the exponential function decreases
Answer:
A function that represents exponential decay is:

`f (x) = 4 (2/3) ^ x`