Problem 108 of 7
Build an exponential model through data points (1,12), (3,48).
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infer growth factor and initial value.
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Data points must determine a positive exponential model f(x)=a*b^x.
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Solution
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1. Use the ratio of outputs over the input change to find the base.
2. Solve for the initial coefficient using one point.
3. Write and verify the exponential function.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Linear models or models that fit only one point.