Question

Which equation models the data?

A. 1/2(x) + 50y = 800
B. y = 800 ⋅ (1/2)ˣ
C. y = 1/2(x) + 800
D. y =800 ⋅ (1/2)^−x

Answer 1

The equation that models the data is B) y = 800 ⋅ (1/2)^x.

Step-by-step explanation:

Based on the given options, the equation that models the data is B. y = 800 ⋅ (1/2)x.

This equation is in the form of an exponential function, where the base is 1/2 and the exponent is x. It represents a decreasing exponential growth, as the base is less than 1.

For example, if we substitute x = 0 into the equation, we get y = 800 ⋅ (1/2)0 = 800 ⋅ 1 = 800. And if we substitute x = 1, we get y = 800 ⋅ (1/2)1 = 800 ⋅ 1/2 = 400, which is half of the previous value.