91Ó°ÊÓ

Use a logarithmic transformation to find \(a\) linear relationship between the given quantities and graph the \mathrm{\\{} r e s u l t i n g ~ l i n e a r ~ r e l a t i o n s h i p ~ o n ~ a ~ l o g - l i n e a r ~ p l o t . ~ $$ y=3 \times 10^{-2 x} $$

Use a graphing calculator to sketch the graphs of the functions. $$ y=x^{3 / 2}, x \geq 0 $$

Use a logarithmic transformation to find \(a\) linear relationship between the given quantities and graph the \mathrm{\\{} r e s u l t i n g ~ l i n e a r ~ r e l a t i o n s h i p ~ o n ~ a ~ l o g - l i n e a r ~ p l o t . ~ $$ y=10^{1.5 x} $$

Large areas are often measured in hectares (ha) or in acres. If \(1 \mathrm{ha}=10,000 \mathrm{~m}^{2}\) and 1 acre \(=4046.86 \mathrm{~m}^{2}\), how many acres is 1 hectare?

Use a graphing calculator to sketch the graphs of the functions. $$ y=x^{1 / 3}, x \geq 0 $$

To convert the volume of a liquid measured in ounces to a volume measured in liters, we use the fact that 1 liter equals \(33.81\) ounces. Denote by \(x\) the volume measured in ounces and by \(y\) the volume measured in liters. Assume a linear relationship between these two units of measurements. (a) Find the equation relating \(x\) and \(y\). (b) A typical soda can contains 12 ounces of liquid. How many liters is this?

Use a graphing calculator to sketch the graphs of the functions. $$ y=x^{-1 / 3}, x>0 $$

Use a logarithmic transformation to find \(a\) linear relationship between the given quantities and graph the \mathrm{\\{} r e s u l t i n g ~ l i n e a r ~ r e l a t i o n s h i p ~ o n ~ a ~ l o g - l i n e a r ~ p l o t . ~ $$ v=2 e^{-1.2 x} $$

To convert a distance measured in miles to a distance measured in kilometers, we use the fact that 1 mile equals \(1.609\) kilometers. Denote by \(x\) the distance measured in miles and by \(y\) the distance measured in kilometers. Assume a linear relationship between these two units of measurements. (a) Find an equation relating \(x\) and \(y\). (b) The distance between Los Angeles and Las Vegas is \(434 \mathrm{~km}\). How many miles is this?

Use a graphing calculator to sketch the graphs of the functions. $$ y=2 x^{-7 / 8}, x>0 $$