Question

Population
200-
175-
Option 1
150-
125-
100-
Option 21
757
50-
Option 4
25-
0+
0
1
2
3
Option 3
x
6
7
8
9
10
Time in Years
A herd of zebras is declining at a rate of 4% each year. The herd currently has 72 zebras. Of the four functions graphed in the image, which correctly models the population decline?

Option 4
Option 3
Option 2
Option 1

Answer 1

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.