In 1995, there were 5,400 cell phone users in the city of Northridge. The following year, there were 7,830 cell phone users in the city.
Let t represent the number of years since 1995. Assuming the number of cell phone users increased exponentially, which expression best models the number of cell phone users in Northridge over time?
According to this model, how many cell phone users did Northridge have in 2000?
Round your answer to the nearest whole number.
cell phone users
The expression that best models the number of cell phone users in Northridge over time is given by:
N(t) = A * e^(k*t), where A is the initial number of cell phone users and k is the growth rate.
Let's assume t = 0 represents the year 1995. Therefore, A = 5400.
To find the growth rate (k), we can use the formula:
k = ln(N(t+1)/N(t)), where N(t) is the number of cell phone users in the current year (t) and N(t+1) is the number of cell phone users in the next year (t+1).
Using the given information from 1995 and 1996:
k = ln(7830/5400) = 0.4013
Therefore, the expression becomes:
N(t) = 5400 * e^(0.4013 * t)
To find the number of cell phone users in 2000 (t = 5), we substitute t = 5 into the expression:
N(5) = 5400 * e^(0.4013 * 5)
N(5) ≈ 5400 * e^(2.0065)
N(5) ≈ 5400 * 7.4493
N(5) ≈ 40,274.92
Rounded to the nearest whole number, Northridge had approximately 40,275 cell phone users in 2000.