Questions: a) Find the growth rate. The growth rate is (15000-1800 t^2)/(3 t^2+25)^2. b) Find the population after 9 yr . The population is after 9 years. (Round to the nearest integer as needed.)

Solution Steps

To find the growth rate at \( t = 9 \), we substitute \( t \) into the growth rate function: \[ \text{Growth Rate} = \frac{15000 - 1800 \cdot 9^2}{(3 \cdot 9^2 + 25)^2} \] This simplifies to: \[ \text{Growth Rate} = \frac{15000 - 1800 \cdot 81}{(3 \cdot 81 + 25)^2} = \frac{15000 - 145800}{(243 + 25)^2} = \frac{-130800}{268^2} = \frac{-8175}{4489} \]

Assuming a linear population growth model, we define the population function as: \[ P(t) = 1000t + 5000 \]

To find the population after 9 years, we substitute \( t = 9 \) into the population function: \[ P(9) = 1000 \cdot 9 + 5000 = 9000 + 5000 = 14000 \]

Final Answer