The average growth rate of the population of a certain city is 7.5% per year. The city's population is now 22,750 people. What is the expected population in 10 years?
I was always taught this formula for exponential growth
N(t) = N_0 e^(kt)
N = population
N_0 = population at t(0)
e = 2.7...
k = some positive constant
t = time
Here's what my teacher wrote on my paper for the formula
f(x) = C(1 + r)^x
f(x) = population
C = initial population
r = growth rate
The Attempt at a Solution
no i dont understand how to do this exactly because I don't know what to use for the constant k
so i used the second one
22750 (1 + .075)^10 = 46888.4680
now what I don't udnerstand is that this really makes no sense at all becasue if I wanted to fidn the population at 10 minutes or ten centuries and just plugged in 10 into the equation with no units at all I would get the same exact answer. Can youp please tell me how to go about reasoning this out... THANKS!