There Were 1403 Million Licensed Drivers In Florida In 2009 And 1315 There were 14.03 million licensed drivers in Florida in 2009 and 13.15 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the number of years since 2004, assuming growth is....
Paper For Above instruction To derive the formulas for the number of licensed drivers in the United States as a function of time, we first interpret the given data and assumptions. The problem indicates that the number of licensed drivers in Florida is known for specific years, and we are asked to model the overall US licensed driver population based on these data points. While the initial data refers specifically to Florida, we will proceed under the reasonable assumption that Florida’s growth trends can serve as a proxy or foundation for understanding US-wide growth patterns, especially since exact national data points are not provided. Let t represent the number of years since 2004, making t=0 correspond to the year 2004. The known data points are: In 2004 (t=0): N = 13.15 million In 2009 (t=5): N = 14.03 million Using these data points, we will construct both a linear and an exponential model for N(t). Part A: Linear Model The general form of a linear model is: N(t) = at + b Where: b is the initial value when t=0 a is the annual growth rate in millions per year Given that N(0) = 13.15 million drivers, we find: b = 13.15 Next, we use the second data point (t=5, N=14.03) to solve for a: