91Ó°ÊÓ

Given that \(n\) represents a positive integer, decide whether each statement is sometimes true, always true, or never true. If it is sometimes true, state for what values it is true. \(4^{n}\) is less than \(1,000,000\left(\text { that is, } 4^{n}<1,000,000\right)\)

Life Science The data in each table represent how a certain population of bacteria grows over time. Identify the growth factor for each table, assuming the growth is exponential. $$ \begin{array}{|c|c|}\hline \text { Hours from Start } & {\text { Population }} \\\ \hline 25 & {3 \times 10^{8}} \\ {26} & {6 \times 10^{8}} \\ {27} & {1.2 \times 10^{9}} \\ \hline\end{array} $$

Find the indicated roots without using a calculator. $$ \sqrt{0.0064} $$

Given that \(n\) represents a positive integer, decide whether each statement is sometimes true, always true, or never true. If it is sometimes true, state for what values it is true. \(0.9^{n}\) is greater than or equal to \(0,\) and at the same time \(0.9^{n}\) is less than or equal to 1 (that is, \(0 \leq 0.9^{n} \leq 1 )\)

Find the indicated roots without using a calculator. $$ (\sqrt{26})^{2} $$

The population of frogs in Kyle's family's lake is \(1,000\) this year. a. If the population decreases by 24\(\%\) a year, what number can Kyle multiply this year's population by to estimate the frog population in the lake next year? b. If the population decreases by 6.9\(\%\) a year, what number can Kyle multiply this year's population by to estimate the frog population in the lake next year?

For what positive values of \(x\) will \(x^{20}\) be greater than \(x^{18} ?\)

Find the indicated roots without using a calculator. $$ (\sqrt{0.09})^{2} $$

For what positive values of \(x\) will \(x^{18}\) be greater than \(x^{20} ?\)

Find the indicated roots without using a calculator. $$ \sqrt{(-3)^{2}} $$