Let's solve each part of the problem step by step.

Given:

The growth model for the population is: $A = 5e^{0.001t}$ where $A$ is the population in millions, and $t$ is the time in years after 2003.

Part a: Finding the Growth Rate

The growth model can be written in the form $A = A_0 e^{kt}$, where $k$ is the growth rate. In this case, $k = 0.001$.

To convert $k$ into a percentage: $0.001 \times 100 = 0.1\%$ So, the country's growth rate is 0.1%.

Part b: Time to Double the Population

To find the time it takes for the population to double, we use the formula: $t = \frac{\ln 2}{k}$ Substitute $k = 0.001$: $t = \frac{\ln 2}{0.001} \approx \frac{0.693}{0.001} = 693$ Therefore, it will take approximately 693 years for the country to double its population.

Would you like more details on any of these calculations or have other questions?

Related Questions:

1. How does changing the growth rate affect the doubling time?
2. What is the general formula for population growth in an exponential model?
3. How would the model change if the initial population were different?
4. What would the doubling time be if the growth rate was 0.5%?
5. How can you determine the half-life of a population with a negative growth rate?

Tip:

In exponential growth models, small changes in the growth rate can significantly affect the doubling time due to the nature of exponential functions.