Find the percent change of f(x) =2(1 - .2)^-x

Question

Nearest percent.

Answer 1

f(x) = 2(1 - 0.2) ^-x

f(x) = 2(0.8)^-x

 

The percent change is computed over an interval, which you don't specify.  I will choose a general interval between x and x+a:

 

% change = (Ending Value - Starting Value)/(Starting Value)

 

     = ((f(x+a)-f(x))/f(x)

 

     = (2*(0.8)^-(x+a) - 2*(0.8)^-x)/2*(0.8) ^-x

 

     = (2*(0.8)^-x*(0.8)^-a - 2*(0.8)^-x) / 2*(0.8)^-x

 

     = 2*(0.8)^-x(0.8^-a - 1)/2*(0.8)^-x

 

     = (1/0.8^a) - 1

 

For a = 2, for example:

 

    % Change = (1/0.8²) - 1 = (1/0.64) - 1 = 1.5625 - 1 = 0.5625 = 56.25% increase (rounds to 56%)