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