The original functions are: f(n) = 500 and g(n) = [9/10]^(n-1)
A geometric sequence combining them is: An = f(n)*g(n) = 500*[9/10]^(n-1):
Some terms are:
A1= 500
A2 = 500*[9/10]
A3 = 500*[9/10]^2
A4 = 500*[9/10]^3
....
A11 = 500*[9/10]^10 ≈ 174.339
Answer: the third option, An = 500[9/10]^(n-1); A11 = 174.339
The inverse of a function is determined by substituting f(x) by y and expressing the function in terms of x = ... Then exchange the places of x and y. In this problem, y = 0.5 x -1; x = 2(y+1) . Then g(x) = y = 2x +2. The graphs are linear but g(x) has a larger slope compared to f(x).
