Answer:
[tex]f(x) = 5120(\frac{5}{4}) ^{x}[/tex]
Step-by-step explanation
[tex]f(x) = a(b)^{x}[/tex] f(x) = 5120 when x = 0
5120 = [tex]a(b)^{0}[/tex] = a
Now
[tex]f(x) = 5120(b)^{x}[/tex] f(x) = 6400 when x = 1
6400 = 5120[tex](b)^{1}[/tex]
6400/5120 = b
b = 5/4
So, [tex]f(x) = 5120(\frac{5}{4}) ^{x}[/tex]
