Final answer:
To determine the best-fit exponential equation for Harry's arcade visitation data, regression analysis through technology is necessary. The predictions for each option provided can be calculated using the exponential growth factor. The option with growth that aligns most closely to the observed data pattern is likely the correct answer.
Step-by-step explanation:
To determine the exponential equation that best represents Harry’s arcade visitor data, we can use a process similar to regression analysis, though this example requires technology like a graphing calculator or statistical software which is not demonstrated here. However, based on the choices provided, the equation and prediction should align reasonably with the pattern in the data.
To make an accurate prediction, we compare each option's base growth factor to the increase seen in the visitor counts. When we compare the monthly increases in visitor counts, we can see that the growth does not appear to double each month, which eliminates the fastest growth option. Instead, we're looking for growth that is steady but less extreme.
Examining the provided options and applying the exponential model to predict the number of people who might visit after 6 months would look something like this for option A:
f(x) = 126(1.4)^x
After 6 months (x=6):
f(6) = 126(1.4)^6 ≈ 949 people
We would repeat this calculation for each of the other options to find the most reasonable fit based on the actual data. The closest match to the observed pattern in the visitor data would be the most likely correct answer.