Question

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?

Explanation:

Step1: Recall the formula for exponential decay

The formula for exponential decay is \( P(t)=P_0(1 - r)^t \), where \( P_0 \) is the initial population, \( r \) is the rate of decay, and \( t \) is the time in years. Here, \( P_0 = 72 \) and \( r=0.04 \). So the function is \( P(t)=72(0.96)^t \).

Step2: Analyze the shape of the exponential decay function

An exponential decay function \( y = a(b)^x\) (\(0 < b<1\)) has a characteristic shape. It starts at \( y = a\) when \( x = 0\) and decreases as \( x\) increases. Among the four - option graphs, we need to look for a curve that starts at \( (0,72)\) (or close to it, considering possible graph - scaling) and has a decreasing trend that is not linear (since it's an exponential, not a linear function \(y=mx + c\)).

Answer:

Option 4 (assuming Option 4 is the graph that represents the exponential decay function \(P(t)=72(0.96)^t\) with the correct starting point and decreasing - curve shape).