Question 253143
{{{y=a*b^x}}} Start with the general exponential equation



{{{4=a*b^20}}} Plug in x=20 and y=4 since the point (20,4) lies on the graph.



{{{4/b^20=a}}} Divide both sides by {{{b^20}}} to isolate 'a'.



{{{a=4/b^20}}} Rearrange the equation.



{{{y=a*b^x}}} Go back to the general exponential equation



{{{3=a*b^25}}} Plug in x=25 and y=3 since the point (25,3) also lies on the graph.



{{{3=(4/b^20)*b^25}}} Plug in {{{a=4/b^20}}}



{{{3=(4b^25)/b^20}}} Multiply



{{{3=4b^5}}} Reduce.



{{{3/4=b^5}}} Divide both sides by 4.



{{{root(5,3/4)=b}}} Take the 5th root of both sides to isolate 'b'.



{{{(3/4)^(1/5)^""=b}}} Convert to exponential notation.



{{{b=(3/4)^(1/5)^""}}} Rearrange the equation.



{{{a=4/b^20}}} Go back to the previously isolated equation.



{{{a=4/((3/4)^(1/5))^20}}} Plug in {{{b=(3/4)^(1/5)^""}}}



{{{a=4/((3/4)^4)}}} Multiply and simplify the exponents.



{{{a=1024/81}}} Simplify and reduce.



So the exponential equation that goes through the points (20,4), (25,3) is {{{y=(1024/81)(3/4)^(x/5)}}}