To determine which function correctly models the population decline of the zebra herd that decreases at a rate of 4% annually, we can use the formula for exponential decay:
\[ P(t) = P_0 \cdot (1 - r)^t \]
Where:
- \( P(t) \) is the population at time \( t \)
- \( P_0 \) is the initial population (72 zebras in this case)
- \( r \) is the decay rate (4% or 0.04)
- \( t \) is the time in years
Plugging in the values:
\[ P(t) = 72 \cdot (1 - 0.04)^t \] \[ P(t) = 72 \cdot (0.96)^t \]
Now we need to see which option has a function that looks like \( P(t) = 72 \cdot (0.96)^t \).
The options you have provided are not explicitly defined here, but if any of the functions corresponds to this formula, that’s the one that models the population decline correctly.
Summary:
Please check each option for a function similar to \( P(t) = 72 \cdot (0.96)^t \) to identify which one fits best. The correct option should show a decay behavior consistent with 4% loss per year starting from 72 zebras.
1 answer