Have you ever been swimming in a pool, and your eyes were red when you get out? this means the chemicals in the pool were not adjusted correctly! more specifically, the measurement of the pool's ph was not quite right.

ph is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. the variable x represents the amount of hydronium ions, and f(x) gives the ph level.

different liquids have ideal ph values that are different. water at 25 degrees celsius has a ph of 7. anything that has a ph less than 7 is called acidic, and a ph above 7 is basic, or alkaline. seawater has a ph just more than 8, whereas lemonade has a ph of approximately 3.

create a graph of the ph function either by hand or using technology. locate on your graph where the ph value is 0 and where it is 1. you may need to zoom in on your graph.
use your graph to find the ideal ph level if the amount of hydronium ions is raised to 0.50.
the pool company developed new chemicals that transform the ph scale. using the ph function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. you may graph by hand or using technology. be sure to label each transformation on the graph.
f(x) + 1
f(x + 1)

In each bouquet of flowers, there are 2 roses and 3 white carnations. complete the table to find how many roses and carnations there are in 2 bouquets of flowers.

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

Which function has an inverse function? a. f(x)= |x+3|/5 b. f(x)= x^5-3 c. f(x)= x^4/7+27 d. f(x)= 1/x²