A(t)=P(1/2)^t/h
In the given equation, A(t) represents the amount of a substance at time t, P is the initial amount of the substance, and h is a constant value
In the given equation, A(t) represents the amount of a substance at time t, P is the initial amount of the substance, and h is a constant value.
To understand this equation, let’s break it down:
1. Exponential Decay: The equation represents exponential decay, where the amount decreases over time. The base of the exponential function is 1/2, which means the substance is decreasing by half each time period.
2. The Exponent: The exponent in the equation is t, representing time. As time increases, the exponent becomes larger, resulting in a smaller value for (1/2)^t. This causes the amount of the substance to decrease exponentially.
3. Initial Amount: The initial amount of the substance is denoted by P. This is the amount of the substance at the beginning or at t=0.
4. The Constant h: The constant h determines the rate of decay. It represents the time it takes for the substance to decrease to half its initial amount. For example, if h is 5, after 5 time units, the substance would have decayed to half its initial amount.
To summarize, the equation A(t) = P(1/2)^t/h represents exponential decay, where the amount of a substance continuously decreases over time. The initial amount is given by P, the time is represented by t, and the constant h determines the rate at which the substance decays.
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