Question

Drag each inequality or statement to the correct location on the table. Not all inequalities will be used.

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 could be used to find in which year of employment each woman surpasses a salary of $45,000. Then decide which statement is true for each person.

Answer 1

Jessica's Salary

- Her salary surpasses $45,000 in the 8th year

- 36,000 ( 1.031 )^t > 45,000

Morgan's Salary

- Her salary surpasses $45,000 in the 7th year

- 38,000 ( 1.025 )^t > 45,000

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Explanation:

Answer 2

Let

t---------> the time in years

y--------> the salary in dollars

we know that

Jessica's salary

`y=36,000(1.031)^(t)`

`y> 45,000`

so

`36,000(1.031)^(t) > 45,000`

`(1.031)^(t) > 1.25`

Solve for t

applying log both sides

`t*log(1.031) > log(1.25)`

`t > 7.31\ years`

Morgan's salary

`y=38,000(1.025)^(t)`

`y> 45,000`

so

`38,000(1.025)^(t) > 45,000`

`(1.025)^(t) > 1.18`

Solve for t

applying log both sides

`t*log(1.025) > log(1.18)`

`t > 6.85\ years`

therefore

the answers are

Jessica's salary

a) The inequality is equal to ----->
`36,000(1.031)^(t) > 45,000`

b) Her salary surpasses
`\$45,000` in the 8th year

Morgan's salary

a) The inequality is equal to ----->
`38,000(1.025)^(t) > 45,000`

b) Her salary surpasses
`\$45,000` in the 7th year