4. The equation A=1500(.965)^t models the decline of a species of bird known as the Quetzal. a. What is the decay factor? __ b. What is the current percent rate of decrease (% ) for this species annually? __

## Step 1The given equation is \(A=1500(.965)^{t}\). This is an exponential decay model, where is the amount of the species remaining after years, 1500 is the initial amount of the species, and.965 is the decay factor.## Step 2The decay factor is the base of the exponent in the equation, which in this case is.965.## Step 3To find the annual percent rate of decrease, we subtract the decay factor from 1 and multiply by 100 to convert it to a percentage.### **The formula for the annual percent rate of decrease is:**### \( (1 - \text{decay factor}) \times 100 \)## Step 4Substitute the decay factor into the formula:### \( (1 -.965) \times 100 = 3.5\% \)