The amount of water used in a community increases 24% over a 7 year period. Find its annual growth factor b and annual percent growth rate r

Question

The amount of water used in a community increases 24% over a 7 year period. Find its annual growth factor b and annual percent growth rate r

Answer 1

P =  P₁* e^rt, where P is population of t years, P₁ is population of starting year, r is growth rate, and t is time

Here no population given, only 24% increased.  So if p₁=1, then P= 1.24. 

Therefore, p/p₁ = e^rt = 1.24, where t=7. 

Then, e^7r= 1.24. 

Take ln on both side, 7r= ln 1.24;  r= ln(1.24)/7 = 0.03073;

Growth rate =  0.03073 = 3.073% 
Let growth factor g, then g⁷ = 1.24, and g= (1.24)^(1/7) = 1.0312 = 103.12%

Growth factor = 1.0312 = 103.12%