Final answer:
The model used to capture the decreasing or increasing marginal effects of a variable is Polynomial regression. It can fit data curvatures, handle non-linear relationships, and show how marginal effects change at different levels of the independent variable.
Step-by-step explanation:
The model used to capture decreasing or increasing marginal effects of a variable is d) Polynomial regression. Unlike linear regression, polynomial regression can fit data with curvatures and can model the relationship between the independent variable and dependent variable when it is not strictly linear. Thus, it is efficient at capturing various degrees of marginal effects, including both increasing and decreasing trends. An example would be a quadratic equation, which can model both concave up and concave down relationships (e.g., diminishing or increasing marginal returns in economics).
By contrast, exponential growth models are used to describe situations where the rate of change increases over time, such as with bacteria growth in a lab. It can capture phenomena where the growth rate itself is proportional to the current value. Logistic regression is typically used for binary outcomes and can model the probability of an event occurring; it is not inherently designed to capture marginal effects in a variable itself.