Madison's salary increases by 1% each year, meaning this is a geometric series problem. The salary in the first year is $73,000, and each subsequent year's salary is 1% higher than the previous year.

Step 1: Formula for the Total Amount Earned

We can use the formula for the sum of a geometric series:

$S_n = a \frac{1 - r^n}{1 - r}$

Where:

• $S_n$ is the total sum of the salaries over 21 years,
• $a$ is the initial salary ($73,000),
• $r$ is the common ratio (1 + 1% = 1.01),
• $n$ is the number of years (21 years).

Step 2: Substitute the values

$S_{21} = 73,000 \times \frac{1 - 1.01^{21}}{1 - 1.01}$

Let's calculate this value.Madison earned a total of $1,696,461 over the 21 years, rounded to the nearest whole number.

Would you like more details on any of the steps? Here are 5 related questions to deepen your understanding:

1. How would the total change if the salary increased by 2% annually?
2. What is the total amount Madison earned after 10 years?
3. Can the same geometric series formula be applied if the salary decreased by a certain percentage each year?
4. How can this problem be modeled graphically over time?
5. What is the total salary earned in the 21st year alone?

Tip: Geometric series are often used to model scenarios involving steady percentage growth, like salary increments or compound interest.