To determine the annual growth rate of the population in percentage terms, given the function:

$f(x) = 21 \cdot e^{0.75x},$

we follow these steps:

1. Understand the formula:

   • The growth rate is derived from the exponent of $e^{kx}$, where $k = 0.75$.
   • The base $e$ represents continuous growth, and $k$ is the continuous growth rate per unit of time.

2. Convert the continuous growth rate to percentage:

   • The continuous growth rate $k = 0.75$ translates directly into an annual growth rate in decimal form.
   • To convert it to a percentage: Multiply $k$ by $100$: $\text{Annual growth rate} = 0.75 \cdot 100 = 75\%.$

Final Answer:

The population grows by 75% per year.

Let me know if you need further explanation or have additional questions! Here are some related questions to expand on:

1. How does the growth function change if the growth rate $k$ is altered?
2. What is the population after 5 years according to the given function?
3. How can we calculate the doubling time for this population growth?
4. What happens to the population if the growth rate decreases to $k = 0.5$?
5. How would this model be different if the growth was not exponential?

Tip: Exponential growth models are highly sensitive to the growth rate $k$; small changes can lead to significant differences over time.