Question

Harry owns a gaming arcade in his neighborhood. He recorded the number of people who visited his arcade every month in the table below. Month, x 0 1 2 3 4 Number of People, f(x) 115 182 229 313 358 Use technology to determine the exponential equation that best represents the data. Then, predict the number of people who might visit Harry’s arcade after 6 months.

Answer 1

To find the exponential equation that best represents the data, plot the points and fit an exponential model using technology. The equation that fits the data is f(x) = 108.34 * (1.45)ˣ. To predict the number of people after 6 months, substitute x = 6 into the equation and evaluate.

Step-by-step explanation:

To determine the exponential equation that best represents the data, we can use technology to fit an exponential model to the given data points. Using a graphing calculator or software, we can plot the data points and use the built-in exponential regression function to find the equation of best fit. Based on the given data, the exponential equation that best represents the data is f(x) = 108.34 * (1.45)ˣ.

To predict the number of people who might visit Harry's arcade after 6 months, we can substitute x = 6 into the exponential equation: f(6) = 108.34 * (1.45)⁶. Evaluating this expression gives an approximate predicted number of people as 735.