Let's disect our equation.
[tex]P_t = 2000*1.05^t[/tex]
The 2000 is the initial number. Each year, there is 5% more. Add that to the 100% already there and you get 105%, in decimal form 1.05. Each year that is multiplied onto 2000, so we represent it as an exponent ^t. The 1.05^t is our rate of change.
Now let's try for 2 and 5.
[tex]P_2 = 2000*1.05^2[/tex]
[tex]P_5 = 2000*1.05^5[/tex]
The rate of change would be the difference between the two.
[tex]1.05^5 - 1.05^2 = 1.05^(^5^-^2^) = \boxed{1.05^3\ or\ 1.157625}[/tex]
