For the function f (x) = C ∙ a^x the following relation applies:
f(6) / f(4) = 0.25
f(2) - f(3) = 20000
Solve f(5)
Solve f(x) = 625
f(6) = C a^6
f(4) = C a^4
f(6) /f(4) =a^(6-4) = a^2= 0.25
so
a = +/- 0.50
f(2) - f(3) = C (a^2-a^3) = 20,000
C a^2(1 - a) =20,000
if a=+.5
.25 C = 40,000
C = 160,000
if a = -.5
.25 C (1.5) = 40,000
C = 106,666
if a = .5 (just doing this one)
f(x) = C .5^x
at x = 5
f(5) = 160,000 (.5)^4 = .0625*160,000 = 10,000
f(x) = 625
160,000 (.5)^n = 625
.5^n = 0.00390625
n log .5 = log 0.00390625 = -2.408239965
n = -2.408239965 / - 0.301029995
n = 8