equation best describes exponential decay

a. y=a.b(x) with o<b<1

b. y=a.b(x) with o<b_<1

c. y-a.b(2) with o<x_<1

d. y=a.b(x) with a>o

The equation that best describes exponential decay is option a) y = a*b^x with 0<b<1.

Exponential decay refers to a process where a quantity decreases over time in a consistent and predictable manner. In this equation, 'a' represents the initial quantity or starting value, 'b' is the decay factor, and 'x' represents the time or the number of periods.

The exponent 'x' in the equation indicates the time or the number of periods elapsed since the start. The value of 'b' being between 0 and 1 is crucial for exponential decay because it ensures that the quantity decreases over time instead of increasing.

When 'b' is between 0 and 1, each successive value of 'b^x' becomes progressively smaller, leading to a continuous decay of the quantity. This decay factor determines the rate at which the quantity decreases over time.

So, option a) y = a*b^x with 0<b<1 best describes exponential decay because it includes the necessary conditions for exponential decay: a starting value 'a', a decay factor 'b' between 0 and 1, and the exponent 'x' representing the time or number of periods.

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