When your teacher wrote ...
f(x) = C(1 + r)^x
f(x) = population
C = initial population
r = growth rate
he/she should have also defined x to be the annual rate.
so when you replaced x with 10 it was understood that it was years, since the r was the rate per year
If you wanted to find out for a time other than years, you would have to change t to that fraction of a year.
e.g. if you only wanted it for 10 months, t = 10/12 or .83333..
if you wanted 10 minutes you would have to find the number of minutes in a year
which is 365*24*60 = 525600
so your exponent for 10 minutes would not be 10 but
the second equation is probably the easier to use for these types of questions.
you could use the first one
N(t) = N0 e^(kt)
here we have to find the value of k first by using one set of data given, that is
when t = 1,
22750(1.075) = 22750e^1k)
e^k = 1.075
k = ln 1.075 = .07232
so N(t) = 22750e^.07232t
so when t=10
N(10) = 22750(e^(.07232)(10))
= 46888.46804 exactly the same as obtained with the other formula.
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