Math 7B. Pattering and Algebraic Reasoning. Spring25 Sample work

Question

Question 1
An employee is starting a job with an annual salary of $40,000. The employee's salary will increase by 3% at the end of each year with the company.
Complete the following prompts.
Do not round or enter any commas in the response.
What is the amount of the raise, in dollars, at the end of the first year? $_____
What will the employee's annual salary, in dollars, be at the end of the first year with the company? $_____
What is the amount of raise, in dollars, at the end of the second year? $______
What will the employee's annual salary, in dollars, be at the end of the second year with the company? $______

Answer 1

To solve the questions regarding the employee's salary and raises, we'll use the initial salary and the percentage increase.

1. Amount of the raise at the end of the first year:

   • The initial annual salary is $40,000.
   • The raise percentage is 3%.
   • Raise in dollars = Initial salary × Raise percentage \[ \text{Raise} = 40000 \times 0.03 = 1200 \] Answer: $1200

2. Annual salary at the end of the first year:

   • We add the raise to the initial salary. \[ \text{New salary} = \text{Initial salary} + \text{Raise} = 40000 + 1200 = 41200 \] Answer: $41200

3. Amount of the raise at the end of the second year:

   • Now the new salary is $41,200.
   • We again apply the 3% raise. \[ \text{Raise} = 41200 \times 0.03 = 1236 \] Answer: $1236

4. Annual salary at the end of the second year:

   • Add this raise to the salary from the end of the first year. \[ \text{New salary} = 41200 + 1236 = 42436 \] Answer: $42436

The final responses are:

1. $1200
2. $41200
3. $1236
4. $42436