Write an equation for the data shown in each table.

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.

step-by-step explanation:

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