Show Attempt History Current Attempt in Progress Your answer is partially correct. A population grows from 11,000 to 16,000 in four years. Round your answers to three decimal places. (a) Assuming the growth is exponential, find the annual growth rate. The annual growth rate is 9.82 $\%$. (b) Assuming the growth is exponential, find the continuous growth rate. The continuous growth rate is $\mathbf{i}$ + $\%$. eTextbook and Media Hint Save for Later Last saved 1 second ago. Attempts: 6 of 15 used Saved work will be auto-submitted on the due date. Auto-

Step 1 ：The problem provides us with an initial population of 11,000, a final population of 16,000, and a time span of 4 years. We are asked to find the annual growth rate and the continuous growth rate, assuming the growth is exponential.

Step 2 ：For the annual growth rate, we use the formula for exponential growth: \(\text{Final Population} = \text{Initial Population} \times (1 + \text{growth rate})^{\text{number of years}}\). We rearrange this formula to solve for the growth rate: \(\text{growth rate} = ((\text{Final Population} / \text{Initial Population})^{(1 / \text{number of years})}) - 1\).

Step 3 ：Substituting the given values into the formula, we find that the annual growth rate is approximately 9.82%.

Step 4 ：For the continuous growth rate, we use the formula for continuous growth: \(\text{Final Population} = \text{Initial Population} \times e^{(\text{growth rate} \times \text{number of years})}\). We rearrange this formula to solve for the growth rate: \(\text{growth rate} = \ln(\text{Final Population} / \text{Initial Population}) / \text{number of years}\).

Step 5 ：Substituting the given values into the formula, we find that the continuous growth rate is approximately 9.367%.

Step 6 ：Final Answer: The annual growth rate is \(\boxed{9.82\%}\) and the continuous growth rate is \(\boxed{9.367\%}\).