Question

Jessica and Morgan work for different companies. Jessica has a base salary of $36,000 and will receive an increase in salary at a rate of 3.1% per year. Morgan has a base salary of $38,000 and will receive an increase in salary at 2.5% per year.

Jessica and Morgan are calculating the number of years, t, it will take each of them to earn a salary of more than $45,000 at their respective companies.

Determine the inequality that could be used to find in which year of employment each woman surpasses a salary of $45,000.

A. 38,000(1.031)^t > 45,000
B. 36,000(1.025)^t > 45,000
C. 38,000(1.025)^t > 45,000
D. 36,000(1.031)^t > 45,000

Answer 1

Jessica's inequality to determine when her salary exceeds $45,000 is 36,000(1.031)^t > 45,000, and Morgan's is 38,000(1.025)^t > 45,000. These inequalities correspond to Option D for Jessica and Option C for Morgan from the provided choices.

Step-by-step explanation:

The question asks us to determine the inequality that represents when Jessica and Morgan will each earn a salary of more than $45,000 given their respective annual salary increases. To find these inequalities, we need to apply the concept of exponential growth based on their base salaries and growth rates.

Jessica's base salary is $36,000 with an annual salary increase of 3.1%. Therefore, the inequality for Jessica would be 36,000(1.031)^t > 45,000, where t represents the number of years.

Morgan's base salary is $38,000 with an annual salary increase of 2.5%. Thus, the inequality for Morgan would be 38,000(1.025)^t > 45,000, again with t representing the number of years.

Comparing both situations to the answer choices provided, we can see that Jessica's situation matches Option D, and Morgan's matches Option C.