Question

Use the following information. From 1894 to 1903 the number of miles of cable car track decreased by about \(10 \%\) per year. There were 302 miles of track in 1894 . Sketch a graph of the results.

Short answer

The graph will show an exponential decay curve starting at 302 miles in 1894, and decreasing about 10% each year. The curve will show the continuous decrease in the track length over the years from 1894 to 1903. Detailed values for each year were calculated by annually reducing the previous year's distance by 10%.

Step-by-step solution

Decipher the Percentage Decay

First, determine the decay percentage, which in this case is 10%. This means that each year, the amount of cable car tracks shrinks to 90% of its value from the previous year. So, to get the next year's length of tracks, the length of tracks in the current year has to be multiplied by 0.90.

Calculate Values for Each Year

Next, calculate the length of the tracks for each year from 1894 to 1903 using the decay percentage. Start with the length in 1894 which is 302 miles, and multiply it by 0.90 for each subsequent year. Keep the track of the year and the corresponding track length.

Sketch the Graph

On graph paper, make a scatter plot of the year versus the track length. The horizontal axis should represent the years ranging from 1894 to 1903 and the vertical axis should represent the length of the tracks. Mark each year with its corresponding track length on the graph.

Draw the Decay Curve

Lastly, sketch the exponential decay curve through the points in the graph. This curve will show a decreasing trend, reflecting how the length of tracks decreased over the span of 10 years.