Question

determine the base, b, of the exponential model. Is the base a growth or decay factor? a. b is 0.6394; It is a growth factor. b. b is 0.6394; It is a decay factor. c. b is 20.5; It is a growth factor. d. b is 20.5; It is a decay factor.

Answer 1

An exponential model can be described by the function
$f(x) = a(b)^x$
where: a is the initial population or the starting number, b is the base and x is the number of periods elapsed.

When the base of an exponential model is greater than 1 it is called a growth factor, but when it is less than 1 it is called a decay factor.

Given the exponential model
$n=20.5(0.6394)^t$
n is the final output of the exponential model, 20.5 is the starting number, 0.6394 is the base and t is the number of periods/time elapsed.

Here, the base is 0.6394 which is less than 1, hence a decay factor.

Therefore, the base, b, of the exponential model is 0.6394; It is a decay factor.