Due date:_________
____/16
Name: ____________
CP Algebra 2 Unit 7 Project
Unit Topic: Exponential and Logarithmic Functions Lesson Essential Question: How can logarithmic and exponential functions be used in
today’s world? Please Explain.
Problem: The pH system was developed by a Danish Biochemist, Soren Sorensen, in
1909. The symbol pH stands for “potential hydrogen” and is used to describe the
concentration of hydrogen ions in a particular solution. A neutral solution has a pH of 7,
acidic solutions have a pH below 7, and basic solutions have a pH above 7. Distilled
water, for example, has a pH of 7, while human blood under normal conditions should
have a pH between 7.35 – 7.45.
pH can be measured with an electronic pH meter or by using special dyes called acidbase indicators. The concentration of hydrogen ions determines the color of the
indicator. Litmus paper is an example of an acid-base indicator that when dipped in a
solution, turns red if the solution is an acid, or blue if the solution is a base.
Use the following information to answer problems 1-4.
The pH of a person’s blood can be determined using the Henderson-Hasselbach
equation, which is: 𝒑𝑯 = 𝟔. 𝟏 + 𝒍𝒐𝒈
𝒙
𝒚
, where x is the concentration of bicarbonate
and y Is the concentration of carbonic acid.
Task Analysis: Questions you must complete below and show all work:
1. Expand the Henderson-Hasselbach equation.
2. Calculate the pH of a person’s blood if the concentration of bicarbonate is
25.4 and the concentration of carbonic acid is 1.2. Round your result to three
decimal places. Is the person’s pH in the normal range?
Due date:_________
____/16
Name: ____________
3. A person’s blood has a pH of 7.371 and a carbonic acid concentration of 1.5.
Approximate the concentration of bicarbonate in the person’s blood. Round
your result to two decimal places.
4. A person’s blood has a pH of 7.408 and a carbonic acid concentration of 26.4.
Approximate the concentration of carbonic acid in the person’s blood. Round
your result to two decimal places.
5. The formula for Newton’s law of Cooling is 𝑻 = 𝑻𝟎 − 𝑻𝒓 𝒆!𝒓𝒕 + 𝑻𝒓 where t
is the time it will take for a substance to cool to a temperature T, given the
cooling rate r, the initial temperature T0, and the ambient temperature TR,
Solve the formula for t. What does this new formula represent? Show all of
your work & write in complete sentences.
Due date:_________
____/16
Name: ____________
Solve the following equations and show all of your work for full credit
6.
500
100−𝑒𝑥 2
= 20
7.
ln 𝑥 + 5 = ln 𝑥 − 1 − ln (𝑥 + 1)
8.
log 𝑥 + 4 − log 𝑥 = log (𝑥 + 2)
Due date:_________
____/16
Name: ____________
Rubric for Culminating Activity
Unit Topic: Exponential and Logarithmic Functions
Scale
4
3
2
1
Answers all
parts of the
problem
Student
answers 7-8
parts of the
problem
Student
shows some
work and
answers for 78 parts of the
problem
Most (7-8)
calculations
are accurate
and correct
with accurate
explanation
written in
complete
sentences
Student
answers 3-6
parts of the
problem
Student
shows work
for 3-6 parts
of the
problem and
answers
Some (3-6)
calculations
are accurate
and correct
with little or
no
explanation
written in
complete
sentences
Student
answers 0-2
parts of the
problem
Student shows
work for 0-2
parts of the
problem and
answers
Criteria
Completeness
Shows all work
Accuracy in
calculations
Neatness
Student
shows all
work & how it
is calculated
All
calculations
are accurate
and correct
and all
questions are
answered in
complete
sentences
Some or no
calculations
(0-2) are
accurate and
correct and no
explanation or
inaccurate
explanation
written in
complete
sentences
All students
Students work Students work Students work
work is neat &
is neat &
is neat &
is neat &
legible for all
legible for
legible for 3-6 legible for 0-2
parts of the
most (7-8)
parts of the
parts of the
problem
parts of the
problem
problem
problem