Suppose you make $10 an hour at your job that you have been working at for 5 years. Each year, you get a 6% raise.
1. Write an equation that models this situation.
To write an equation that models this situation, let's break it down step by step.
First, let's determine the initial salary, which is $10 an hour. We can represent this as "P" for the initial salary.
Next, we need to account for the 6% raise each year. This means that each year the salary increases by 6% of the previous year's salary. We can represent this as "R" for the raise percentage.
Now, let's consider the number of years worked. In this case, it's 5 years. We can represent this as "t" for the number of years.
Finally, we need to find an equation that relates the initial salary, raise percentage, and number of years worked. The equation should represent the total salary earned after a given number of years.
Using the compound interest formula, we can write the equation as:
Total salary = P * (1 + R)^t
Applying this to the given situation, the equation becomes:
Total salary = $10 * (1 + 0.06)^5
Simplifying further:
Total salary = $10 * (1.06)^5
Total salary = $10 * 1.3382
Therefore, the equation that models this situation is: Total salary = $13.38
Let's call the initial wage as w0, and the number of years as t. The equation that models this situation can be written as:
w(t) = w0 * (1 + r)^t
Where:
- w(t) represents the wage after t years
- w0 represents the initial wage ($10 in this case)
- r represents the percentage raise (6% in this case, so r = 0.06)
- t represents the number of years (5 in this case)