Question

Don Harrison's current salary is ($ 60,000 ) per year, and he is planning to retire 25 years from now. He anticipates that his annual salary will increase by ( $ 3,000 ) each year (to ( $ 60,)

Answer 1

The question involves calculating the predicted salary increases for Don Harrison using an arithmetic sequence formula,

as well as guiding Peter to make a career decision based on salary and tax information related to various jobs and educational qualifications.

Step-by-step explanation:

The question relates to the forecast of Don Harrison's salary increases up till his retirement, which is a mathematical exercise in arithmetic sequences. Considering Don's starting salary is $60,000 and it increases by $3,000 each year, we can predict the future salaries over the course of 25 years.

As an example, in the first year, his salary will be $60,000, in the second year, it will be $63,000 ($60,000+$3,000), and this pattern will continue each year. Over the span of 25 years, this constitutes an arithmetic sequence with a common difference (d) of $3,000 and an initial term (a1) of $60,000.

The nth term of an arithmetic sequence can be calculated using the formula an = a1 + (n-1)d. To find the salary at retirement, the 25th term should be computed (n=25).

Helping Peter make the best decision for his future requires analyzing the salary and tax information provided for various occupations considering factors such as required education, salary potential, and tax implications.