Which Way to Commute, Statistics Problem Example

We will suppose that the number of cars on the first day for 1^st Avenue in the city is Number of cars on first day.

P=98,665

The growth factor is expected to be around 2 for the expected traffic on 1^st Avenue.
A = 2

The time in days are shown to examine the number of cars (C) that are expected to pass along 1^st Avenue based on 1 month, 2 months, and 75 days (2 1/2 months) supposing that each month is made of 30 days.
T=30

C = 98,665*(2^30) = 98665 * 1073741824 = 105,940,737,064,960 total cars

T=60

C = 98,665*(2^60) = 98665 * 1152921504606846976 = 113,753,000,252,034,556,887,040 total cars

T=75

C = 98,665*(2^75) = 98665 * 37778931862957161709568 = 3,727,458,312,258,668,360,074,526,720 total cars

If the growth factor is at a high rate of 2 over the next 75 days that shows that the amount of traffic will gradually continue to increase.  The three formulas show alarming results stating that over the next 75 days the amount of traffic will increase to alarming proportions.  On the 30^th day it is projected that roughly 105,940,737,064,960 total cars will travel on 1^st Avenue.  This already shows a drastic increase from the original 98,665 cars that were counted on the first day.  The 60^th day is projected to have around 113,753,000,252,034,556,887,040 total cars.  This is growing out of hand because of such a high growth rate.  If the growth rate was expected to be 0 or 1, the road would be travelable.  However, with the growth rate at 2, this formula shows that the amount of traffic will become too much for this single road.

This road should not be extremely congested at the beginning of the 2 ½ months; however, over time it will become too congested that traveling on this road is not a viable option.  The commuting path should be taken through a different route because the number of cars will continue to increase so drastically.  On the 75^th day, it is projected that around 3,727,458,312,258,668,360,074,526,720 total cars may be present on this road.  In all reality, it is unlikely that this number of cars will actually try to travel on 1^st Avenue.  As the road becomes congested, most drivers will also seek to find another route to avoid heavy traffic and reduce total travel time.  This is not taken into consideration through this formula.  Nevertheless, it does appear that the number of cars will increase to an alarming number over the next 2 ½ months and this road must be avoided on the total commute.