4) Evaluate without a calculator using the power law of logarithms. \( \begin{array}{ll}\text { a) } \log _{2} 32^{3} & \text { b) } \log 1000^{-2}\end{array} \)

Consider the number pattern below: \[ \frac{-3}{5} ; \frac{-6}{9} ; \frac{-9}{13} ; \ldots . \ldots \] Determine the next two terms of the number pattern. Determine the \( n^{\text {th }} \) term of the number pattern.

Calcula las siguientes potencias: \( \begin{array}{ll}\text { a) } 3^{-4}=\frac{\square}{\square} & \text { b) }(3 / 4)^{-2}=\frac{\square}{\square}\end{array} \)

Determine whether the following statment is true or false. The graph of \( y=\frac{1}{7} g(x) \) is the graph of \( y=g(x) \) stretched by a factor of 7 . Choose the correct answer below. A. True, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate. Balse, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by \( \frac{1}{7}<1 \). C. True, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by 7 and \( 7>1 \). D. False, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate.

A 25 -year old woman burns \( 350-70 t \) cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is \( 135 t \) calories during the \( t \) th hour. What is her net decrease in calories after walking for 4 hours?

5 State which consecutive whole numbers are either side of: \( \begin{array}{lll}\text { a } \sqrt{29} & \text { b } \sqrt{40} & \text { c } \\ \text { 7II }\end{array} \)