Answer:
a) common ratio: 0.8
b) equation: y = 100(0.8^x)
Explanation:
Given the terms of a geometric sequence ...
(x, y) = (0, 100), (1, 80), (2, 64), ...
you want the common ratio and the equation in the form y=a·b^x.
Ratio
The common ratio is the ratio of each term to the previous term:
b = 80/100 = 64/80 = 51.2/64 = 0.8
Multiplier
The value of 'a' in the equation is the value of y when x=0. The table tells you a = 100.
Equation
For a = 100 and b = 0.8, the equation is ...
y = a(b^x)
y = 100(0.8^x)