Short Answer

Comparing Digital Storage Growth Projections

A records specialist at a community health clinic is using exponential functions to project the growth of digital patient files. The baseline growth over xx months is modeled by the function f(x)=2xf(x) = 2^x. After upgrading to a faster intake system, the clinic's digital file growth accelerates and is now modeled by the function g(x)=2x+1g(x) = 2^{x+1}.

When comparing the graphs of these two functions on the same coordinate system to present to the clinic's administration, answer the following:

  1. Identify the specific type, direction, and magnitude of the geometric translation that occurs to the baseline graph of f(x)=2xf(x) = 2^x to produce the new graph of g(x)=2x+1g(x) = 2^{x+1}.
  2. State the yy-value of the new function g(x)g(x) at x=0x = 0 (the starting month), and briefly explain how this output relates to the baseline function's output at x=0x = 0.

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Updated 2026-05-31

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