If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, 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.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool by 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
The pool company developed new chemicals that transform the pH scale. Graph the parent pH function p(t) = −log10t and the transformations below on the same graph. Send the graph to your partner. Your partner will explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences.
p(t) + 1
p(t + 1)
−1 • p(t)
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p(t)=-log(t)
p(.5)=-log(.5)= 0.3
y=-log ^(0.5)
10^-y= 0.5
10
p(t)+1
Red line on graph, this transformation has shifted up by 1. This translation doesn't result in a y-intercept.
p(t+1)
Blue line on graph, this transformation is shifting to the left by 1. This translation results in a y-intercept because it crosses the y-axis.
<span>-1 p(t) </span>
Answer:
the probability of selecting a number less than 10 is 4/9, or 0.44.
Step-by-step explanation:
There are 4 numbers less than 10, out of a total of 9 numbers.
Thus, the probability of selecting a number less than 10 is 4/9, or 0.44.
Answer:
spotted male
Step-by-step explanation:
if you look at the numbers then you will see that this one has the biggest number
Answer:
=3x^7
Step-by-step explanation:
Simplify, 12x^4 ÷ 4 x^3
Cheers! :)
