In 2010, a city's population was 83,075 and it was declining at a rate of \( 1.04 \% \) each year. Which is the best prediction for when the city's population will first be below 62,000 ?

Rationalize the denominator: \( \frac{15}{\sqrt{75}} \) \( A=\square \)

Cabinet \( X \) costs \( \$ 30 \), requires \( 12 \mathrm{sq} \mathrm{ft} \mathrm{of} \mathrm{floor} \mathrm{space} \),and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( Y \).)

7) Simplify the logarithm so that no argument contains a product, quotient or a powe \( \ln \left(e x^{3}\right)= \) a) \( 1-3 \ln x \) b) \( 01+3 \ln x \) c) \( 03-\ln x \) d) \( 3+\ln x \)

Cabinet \( X \) costs \( \$ 30 \), requires 12 sq ft of floor space, and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft ? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( ~ \) .)

3. Given the list of terms \( \frac{1}{3}, 1, \frac{5}{3}, \frac{7}{3}, \ldots \) a) Find the \( 15^{\text {th }} \) and \( -16^{\text {th }} \) term.