please help me with algebra 2 work

Question

write an exponential equation for the sequence below. you may assume that the first term of the sequence is the Y-intercept. 120, 104.4, 90.828, 79.02036

Answer 1

y = a·b^x

where a is the initial value and b is the common ratio. I can't see the y-intercept but I assume it's 120, so a = 120. You get b by taking the ratio of any two successive terms:

b = 104.4/120 = 90.828/104.4 = 79.02036/90.828 = 0.87

Final form:

y = 120·(0.87)^x

Answer 2

This is a geometric sequence, which is just an exponential function with a domain of the natural numbers instead of all reals. The common ratio of the terms, which can be found by dividing any term by the term that precedes it (ie r = t_n+1 / t_n ), corresponds to the base number, b, in the exponential function f(x) = a·b^x. The parameter a represents the y-intercept of the graph (usually the initial amount or population, or something), and we are told to use the 1st term for a.

So, we can represent the sequence using function notation as follows: f(n) = 120·(.87)ⁿ , for n ∈ Ν

You can and should confirm that plugging in 1 for n gives f(1) = 104.4 etc.