Question

This table shows several values of an exponential function.
x f(x)
1
6/7
2
12/49
3
12/343
Write an equation for the function in the form f(x)=a(b)x.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
f(x)=

Answer 1

Use f(2)/f(1) = b:
b = (12/49) / (6/7) = 2/7.
Then a = f(1)/b = (6/7)/(2/7) = 3.

So f(x) = 3(2/7)^x.

(If you plug x=3 this gives 24/343, so the table’s 12/343 is likely a misprint.)