This math topic focuses on solving for time in continuous decay scenarios using exponential functions. Skills practiced include: 1. Understanding and applying the exponential decay model in the form of \( P(t) = P_0 \times e^{rt} \), where \( P(t) \) represents the quantity at time \( t \), \( P_0 \) is the initial quantity, \( r \) is the rate of decay, and \( e \) is the base of the natural logarithm. 2. Calculating the time required for a population or quantity, like whale populations, radioactive isotopes, or bacteria, to decrease from an initial value to a lower value at a given continuous decay rate. 3. Manipulating algebraic and logarithmic expressions to isolate and solve for the variable of interest, which is time in these problems.
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