Answer:
1) f(x) = 500·(1.1)ˣ
2) f(x) = 500·(0.9)ˣ
Step-by-step explanation:
1) The given values in the table are;
x; 0, 1, 2, 3
f(x); 500, 550, 605, 665.5
By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;
550/500 = 11/10 = 1.1 = 605/550 = 665.5/605
From which we have;
The values of f(x) are in a geometric progression
The nth of a geometric progression = a·rⁿ
The common ratio, r = 1.1
The first term, a = 500
The number of terms, n = x
Therefore, xth term, f(x) = a×(r)ˣ
Substituting the values gives;
The equation for the data shown in the table is f(x) = 500·(1.1)ˣ
2) The given table of values is presented as follows;
x; 0, 1, 2, 3
f(x); 500, 450, 405, 364.5
The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405
The terms of f(x) are in a geometric progression
The first term. a = 500
The common ratio, r = 9/10 = 0.9
The nth term of a geometric progression, G.P. = a·rⁿ
By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;
The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.
