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

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

Answer 2

Answer:

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

(got it right on edmentum)

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Step-by-step explanation: