Final answer:
To represent Monica's boutique's annual revenue growth percentage over time as a function, use the function R(n) = 45000 + 2000(n - 1). The annual percentage growth can be calculated with the formula (Increase/Initial Value) * 100% and plotted on a line graph showing the decreasing percentage growth rate over the years.
Step-by-step explanation:
To calculate the annual percentage growth of Monica's boutique's revenue as a function of time, we need to consider that the increase is linear and constant. In the first year, the revenue was $45,000 and it increased by $2,000 each subsequent year. Therefore, the revenue for any year n can be represented by the function R(n) = 45000 + 2000(n - 1), where n represents the number of years since the boutique opened.
To find the annual growth rate as a percentage, we can use the formula for percentage change: Growth Rate = (Increase/Initial Value) * 100%. In the first year, there is no growth since it is the baseline. For the second year and onwards, we calculate the percentage increase from the initial amount. For instance, the growth rate in the second year would be (2000/45000) * 100%, which is approximately 4.44%.
Displaying this data graphically, the x-axis would represent time (years), and the y-axis would represent revenue. Each point on the graph would represent the revenue at the end of each year.