graph \( f(x)=2 \sqrt[3]{x-2+3} \)

Write the following expression as a sum and/or difference of logarithms. Express powers as factors. \[ \ln [e(x+5)] \] \( \ln [e(x+5)]=\square \) (Simplify your answer.)

Suppose that the function \( g \) is defined, for all real numbers, as follows. \( g(x)=\left\{\begin{array}{ll}-\frac{1}{4} x-2 & \text { if } x \leq-2 \\ (x-1)^{2}-2 & \text { if }-2<x \leq 2 \\ 4 & \text { if } x>2\end{array}\right. \) \( g(-3), g(0) \), and \( g(2) \). \( g(0)=\square \)

The half-life of radium is 1690 years. If 40 grams are present now, how much will be present in 860 years? \( \square \) grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

3.3 - Exponents That Are Unit Fractions 1. Complete the table. Use powers of 64 in the top row and radicals or rational numbers in bottom row. \( 64^{1} 64^{\frac{1}{2}} \) 64

Estimate the square root to the nearest (a) integer and (b) tenth. \( -\sqrt{\frac{335}{2}} \) a. nearest integer: \( \square \) b. nearest tenth: