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