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Answer:
Given that a worker earns a 3% increase in her annual salary for each of 5 years, and they plan to continue working in their position for an additional N years, if they continue to earn a 3% increase in their annual salary, to determine what statement could describe the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year the following calculation should be performed:
1 + 0.03 (interest rate) ^ N (number of years) = final interest rate
1.03 ^ N = Final interest rate
Thus, for example, if it were invested for 5 years, the equation would operate as follows:
1.03 ^ 5 = X
1.16 = X
The total percent increase in their annual salary from the first year to the last year is [tex](1.03)^n[/tex].
What is Percentage?
A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is given that the annual salary of the worker increases at a rate of 3%. therefore, the salary of the worker increases compounded at a rate of 3% annually. Therefore, the salary of the worker after n number of years can be written as,
[tex]A = P(1+\dfrac{r}{100})^n[/tex]
where A is the final salary of the worker, P is the initial salary of the worker, r is the rate at which the salary is increasing, and n is the number of years.
Substituting the values in the formula,
[tex]A = P(1+\dfrac{3}{100})^n\\\\A = P(1.03)^n[/tex]
Hence, the total percent increase in their annual salary from the first year to the last year is [tex](1.03)^n[/tex].
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