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? __ c. If the decline continues how many birds will there be in 15 years? __ Round to the nearest whole number A=P(1+(r)/(n))^nt A=Pe^rt

## 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 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. This gives us the percentage decrease.<br /><br />### **The formula for the annual percent rate of decrease is:**<br />### \(r = (1 - \text{decay factor}) \times 100\)<br /><br />## Step 4<br />To find the number of birds after 15 years, we substitute \(t = 15\) into the equation and solve for \(A\).<br /><br />### **The formula for the number of birds after 15 years is:**<br />### \(A = 1500(.965)^{15}\)