The formula for population growth provided in the image is $A = 5e^{0.001t}$, where $A$ represents the population in millions, $t$ is the time in years after 2003, and the exponential growth factor is given by $0.001t$.

Part (a) asks: What is the country's growth rate?

In an exponential growth model of the form $A = A_0 e^{kt}$, the constant $k$ represents the growth rate. In this case, we can see that the exponent is $0.001t$, so $k = 0.001$.

To convert this growth rate into a percentage: $\text{Growth rate} = 0.001 \times 100 = 0.1\%$

Thus, the country's growth rate is 0.1% per year.

Would you like more details on this, or any further explanation?

Here are 5 related questions to expand on this:

1. How do you calculate the time for the population to double using the growth rate?
2. What is the formula for exponential population growth, and how is it derived?
3. If the growth rate were to increase to 0.2%, how would that affect the doubling time?
4. How does the natural logarithm function $\ln$ relate to population growth calculations?
5. What is the difference between continuous and discrete growth models?

Tip:

To find the time it takes for a population to double, you can use the formula $t = \frac{\ln 2}{k}$, where $k$ is the growth rate.