Questions: Megan and Bryce opened a new store called the Donut Pit. Their goal is to reach a profit of 20,000 in their 18th month of business. The table and scatter plot below represent the profit, P, in thousands of dollars, that they made during the first 12 months.

Solution Steps

To solve this problem, we need to analyze the profit data from the first 12 months and predict the profit for the 18th month. We can use linear regression to model the relationship between time (in months) and profit. Once we have the model, we can use it to predict the profit for the 18th month.

To solve the problem, we need to analyze the given data and determine the trend or pattern in the profits over the first 12 months. This will help us predict the profit in the 18th month. Since the problem does not provide the actual data or scatter plot, I will outline the general steps you would take to solve such a problem.

First, examine the table and scatter plot to understand the trend in profits over the first 12 months. Look for patterns such as linear growth, exponential growth, or any other recognizable trend.

Based on the analysis of the scatter plot and table, determine the type of trend. If the data points form a straight line, it suggests a linear trend. If the data points curve upwards or downwards, it might suggest an exponential or quadratic trend.

Once the type of trend is identified, fit an appropriate mathematical model to the data. For a linear trend, use linear regression to find the equation of the line, \( P = mt + b \), where \( P \) is the profit in thousands of dollars, \( t \) is the time in months, \( m \) is the slope, and \( b \) is the y-intercept.

Substitute \( t = 18 \) into the model equation to predict the profit in the 18th month.

Final Answer