Arithmetic 1 HW2

A sequence of numbers starts at \(6\). Each term after the first term is triple the preceding term. If the nth term of the sequence is represented by \(q\), which of the following gives \(q\) in terms of \(n\)?

Which of the following is equivalent to \(\frac{x^{8}b^{-3}}{8}\times\frac{a^{3}}{x^{5}}\)?

What is the sum of the solutions to the equation \(2\left|2x-4\right|+3=13\)?

If \(8^{2x}=2^{5x+4}\), find the value of \(x\).

The function \(f(x)=5000(1.08)^{t-1}\) represents the value, in millions of dollars, of Lao Industries’ holdings by the end of each year from \(1987\) to \(2014\), where t is the number of years after \(1987\). In this context, which of the following is the best interpretation of the statement “\(f(12)\) is approximately \(11,658.19\)”?

A surveyor finds that Pittsburgh’s population grows according to the model \(p(y)=300(0.99)^{y}\), where \(p(y)\) is the population in thousands and \(y\) is the number of years since the start of the survey. Which of the following models best models Pittsburgh’s growth m months after the survey?

What is the value of \((x^{a})^{b}*x^{ab}\)?

The expression \(4\sqrt[3]{4^{6}x^{27}}\cdot \sqrt[7]{3^{7}x^{42}}\) is equivalent to \(ax^{b}\), where \(a\) and \(b\) are constants and \(x>1\). Find \(ab\).