Consider the exponential model shown below y N 0e k x Which

Consider the exponential model shown below.

y = N ₀e ^{k x}

Which of the following is true?
Assume that N ₀ is a positive amount.

Consider the exponential model shown below. y=N0ekx Which of the following is true? Assume that N o is a positive amount. For positive x and positive k the above equation represents a decay model. For positive x and negative k the above equation represents a decay model. O For positive x and negative k the above equation represents a growth model. For positive x and positive k the above equation does not represent a growth model.

Solution

Please follow the data and description :

Decay Model :

In general a quantity is said to be in a state of exponential decay if it decreases at a rate proportional to its current value. Explicitly, this process can be expressed by the following differential equation, where N is the quantity and (lambda) is a positive rate called the exponential decay constant :

dN/dt = -(lambda) N.

N = N 0e -(lambda) N

So for the given equation the model could be predicted if the exponents k, x are any of the negative values, as the x could be only a positive number we need to deal with the k value where it could be changeable over the period of time for the growth or for the deacy model.

So assuming that the N 0 is a positive integer and that the statement for x is apositive number and that for the negative value of k th eequation represents a decay model where the data gets on decreasing with respect to the time.

For the equation to be a growth model the two vales needs to be positive where in we could not find in the given options.

So the answer is OPTION B (For positive x, and negative k the above equation represents a decay model).

Hope this is helpful.