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.

Mobth, 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.
A. f(x)=126(1.4)ˣ : Approximately 949 people might visit Harry's arcade after 6 months.
B. f(x)=125(1.68)ˣ: Approximately 2,810 people might visit Harry's arcade after 6 months
C. f(x)=126(1.23)ˣ Approximately 880 people might visit Harry's arcade after 6 months
D. f(x)=126(1.32)ˣ Approximately 667 people might visit Harry's arcade after 6 months.

Answer 1

To find the best exponential equation for the data and make a prediction for 6 months, one must use statistical software or a graphing tool to fit the points and then apply the resulting equation.

Without such technology, it's not possible to accurately choose between the provided options.

Step-by-step explanation:

The exponential equation that best represents Harry's gaming arcade attendance data must be determined using a tool like curve fitting or regression analysis on the provided data points. Once the best-fitting exponential equation is calculated, we can use it to predict future values like the attendance after 6 months.

The given options suggest different base and rate values for the exponential function in the form of f(x) = a(b)^x. We compare them with the provided data points. To predict the number of people who might visit Harry's arcade after 6 months, we substitute x = 6 into the equation that best fits the data.

Without the technology to calculate the best fit, we cannot confirm which option (A, B, C, or D) correctly predicts the attendance after 6 months.