(Solution) - The general form of an exponential equation y abx -(2025 Original AI-Free Solution)

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The general form of an exponential equation, y = abx, is convenient when you know the y-intercept. Start with f(0) = 30 and f(1) = 27.
This painting, Inspiration Point (2000), by contemporary American artist Nina Bovasso, implies an explosion of exponential growth.
a. Find the common ratio.
b. Write the function f (x) that passes through the two data points.
c. Graph f (x) and g(x) = f (x - 4) on the same axes.
d. What is the value of g(4)?
e. Write an equation for g(x) that does not use its y-intercept.
f. Explain in your own words why y = y1 ( b x-x1 might be called the point-ratio form?