Based on the comparison between the exponential functions $f(x) = 2^x$ and $g(x) = 2^{x-1}$, match each characteristic of the transformation with its correct description.

A data analyst at a startup uses the function $f(x) = 2^x$ to model the exponential growth of the company's active users over $x$ months. To reflect a recent one-month delay in a product rollout, the analyst updates the model to $g(x) = 2^{x-1}$. Based on the rules of function transformations, how is the graph of the new model, $g(x)$, shifted horizontally compared to the original model, $f(x)$?

A small business owner uses the function $f(x) = 2^x$ to model the growth of her customer loyalty program. To reflect a one-month delay in the program's launch, she updates the model to $g(x) = 2^{x-1}$. True or False: Compared to the original graph of $f(x)$, the graph of $g(x)$ is a horizontal translation exactly one unit to the left.

A project manager uses the function $f(x) = 2^x$ to model the exponential growth of a company's data storage needs over $x$ months. To account for a one-month delay in a new department's opening, the model is adjusted to $g(x) = 2^{x-1}$. Compared to the original graph of $f(x)$, the graph of the adjusted model $g(x)$ represents a horizontal translation of one unit to the ____.

Horizontal Shift in Exponential Growth Modeling

An operations coordinator at a local shipping center is updating a package-volume forecast chart on a team dashboard. The original forecast is modeled by the base function $f(x) = 2^x$, where $x$ represents time in weeks. Due to a 1-week processing delay, the coordinator must graph the updated model, $g(x) = 2^{x-1}$, on the same coordinate plane.

To construct the new graph efficiently by shifting the base graph rather than plotting every point individually from scratch, arrange the following steps in the correct chronological order.

Analyzing Horizontal Shifts in Marketing Growth Projections