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? Answer choices
a. 7,830(1.45)^t
b. 5,400(0.45)^t
c. 5,400(1.45)^t
d. 7,830(0.45)^t
According to this model, how many cell phone users did Northridge have in 2000? Round your answer to the nearest whole number.
Blank cell phone users
To find the equation that best models the number of cell phone users in Northridge over time, we can use the exponential growth formula:
N(t) = N₀ * e^(rt)
Where:
N(t) = the number of cell phone users at time t
N₀ = the initial number of cell phone users
r = the growth rate
e = Euler's number
t = time in years since 1995
Given that there were 5,400 cell phone users in 1995 and 7,830 cell phone users in 1996, we can substitute these values into the equation to find the growth rate (r).
5,400 = N₀ * e^(r*0)
7,830 = N₀ * e^(r*1)
Dividing the second equation by the first equation, we get:
7,830/5,400 = e^(r*1)/e^(r*0)
1.45 ≈ e^r
Therefore, the equation that best models the number of cell phone users in Northridge over time is:
N(t) = 5,400 * 1.45^t
To find the number of cell phone users in 2000 (5 years after 1995), we can substitute t = 5 into the equation:
N(5) = 5,400 * 1.45^5 ≈ 9,553.75
Rounding to the nearest whole number, Northridge had approximately 9,554 cell phone users in 2000.