To find the number of customers in month 25 using the given model \( y = 6x^2 + 75x + 200 \), we can substitute \( x = 25 \) into the equation.
Now, let's calculate it step-by-step:
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Substitute \( x = 25 \) into the equation: \[ y = 6(25^2) + 75(25) + 200 \]
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Calculate \( 25^2 \): \[ 25^2 = 625 \]
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Now, calculate \( 6(625) \): \[ 6(625) = 3750 \]
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Next, calculate \( 75(25) \): \[ 75(25) = 1875 \]
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Now, we can substitute these values back into the equation: \[ y = 3750 + 1875 + 200 \]
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Finally, add the values together: \[ y = 3750 + 1875 + 200 = 5825 \]
It seems I made a mistake while interpreting the model. Let's check if any of the options match our calculations. The calculations yield \( 5825 \), which is not listed in your options. However, the number \( 58251 \) could be considered an error if we miscalculated the original function's constants or if there was a misinterpretation of the coefficients.
Based on \( y = 6(25^2) + 75(25) + 200 \) with actual calculations, the number of customers for month 25 correctly computes to 5825 based on the mathematical interpretation of the polynomial but does not correspond with any of the answer choices provided.
Please verify the coefficients or check if the model has changed for accuracy.