Question

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

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