Questions: The model below is used to represent a given situation, in which (t) is the independent variable. What type of model is it? [ F=C(1.08)^t ] Linear Exponential Quadratic None of these

The model below is used to represent a given situation, in which (t) is the independent variable. What type of model is it?
[ F=C(1.08)^t ]
Linear
Exponential
Quadratic
None of these

Transcript text: 1 2 points The model below is used to represent a given situation, in which $t$ is the independent variable. What type of model is it? \[ F=C(1.08)^{t} \] Linear Exponential Quadratic None of these

Solution

Solution Steps

The given model $ F = C(1.08)^t $ is in the form of $ a \cdot b^t $, which is characteristic of an exponential model. The base of the exponent, 1.08, indicates growth.

Step 1: Identify the Model Type

The given equation is $ F = C(1.08)^t $. This equation is in the form $ a \cdot b^t $, where $ a = C $ and $ b = 1.08 $. This structure indicates that the model represents exponential growth.

Step 2: Confirm the Characteristics of the Model

In an exponential model, the variable $ t $ is in the exponent, which signifies that as $ t $ increases, $ F $ grows at a rate proportional to its current value. The base $ 1.08 $ indicates a growth factor of 8% per unit increase in $ t $.