MATH SOLVE

2 months ago

Q:
# SOMEBODY PLZ HELP NUMBER 2If 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 3.1.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.2.The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 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.3.The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.p(t) + 1p(t + 1)−1 • p(t)

Accepted Solution

A:

1) using a graphic tool
see attached figure
n1
ph=0----->
for t=0.1
ph=1--------
> for t=0.01
2) using a graphic tool
see attached figure
n2
for
t=0.5------------------ > ph=-0.699
p(t) = −log10t------------------
> y= −log10tconvert the
logarithmic function into an exponential function
we have
10^y = 10^(-log(t)) ------------
> 10^(y) =
1/t ---------- > t = 10^(-y)

t = 10^(-y) 3) p(t) = −log10t which transformation results in a y-intercept (t=0) case

a) p(t) + 1

p(t) = −log10t +1 Still here you can not have a Y intercept (t can't =0) since you would still have log(0) which is forbidden b) p(t + 1)

p(t) = −log10(t+1)

Here of course t can be zero since that just gives you log(1). So you have a Y-intercept. using a graphic tool see attached figure n3b for t=0------------------------ph=-0.9 c) −1 • p(t) p(t) = log10t Still here you can not have a Y intercept (t can't =0) since you would still have log(0) which is forbidden

t = 10^(-y) 3) p(t) = −log10t which transformation results in a y-intercept (t=0) case

a) p(t) + 1

p(t) = −log10t +1 Still here you can not have a Y intercept (t can't =0) since you would still have log(0) which is forbidden b) p(t + 1)

p(t) = −log10(t+1)

Here of course t can be zero since that just gives you log(1). So you have a Y-intercept. using a graphic tool see attached figure n3b for t=0------------------------ph=-0.9 c) −1 • p(t) p(t) = log10t Still here you can not have a Y intercept (t can't =0) since you would still have log(0) which is forbidden