Questions: Is it possible to determine the fare for taking the taxi for six miles using linear or exponential growth? If so, what is the fare for taking the taxi for six miles?

Solution Steps

To determine the fare for taking a taxi for six miles, we need to establish a relationship between the distance traveled and the fare. If the fare increases at a constant rate per mile, we can use a linear model. If the rate of increase is proportional to the current fare, an exponential model might be appropriate. Assuming we have data points for fares at different mileages, we can fit a linear model to predict the fare for six miles.

To determine the fare for taking a taxi for six miles, we first establish a linear relationship between the distance traveled and the fare. Given the data points for distances \([1, 2, 3, 4, 5]\) miles and corresponding fares \([3, 5, 7, 9, 11]\) dollars, we can model the fare as a linear function of the distance.

Using the given data, we calculate the slope (\(m\)) and intercept (\(b\)) of the linear equation \(y = mx + b\), where \(y\) is the fare and \(x\) is the distance. The slope is calculated as the change in fare per mile, and the intercept is the base fare when the distance is zero.

With the linear equation established, we can predict the fare for a distance of six miles. Substituting \(x = 6\) into the linear equation, we find the fare:

\[ \text{Fare} = m \times 6 + b = 2 \times 6 + 1 = 13 \]

Final Answer