Chapter 5 Group Work Exp/Log Lab
As a Lab Tech at University doing research, at 9:00am in the lab you notice a single cell bacteria in a jar, within a
moment, the bacteria triples. Fascinated you watch and in the next moment, the three become nine, then after a
moment the nine become 27, and so on. You created a table to log these results, but you misplaced it. Can you
recreate it here?
1.
2.
Moment
of time
0
1
2
3
4
5
6
7
8
9
Bacteria
count
Write the function that models this bacteria population as a function of time. State the domain and range of this
function. F(t) = ________________ Domain: _______________ Range: _________________
3.
Rapid population growth of the bacteria leads to a problem, they begin to run out of space. Examining the
capacity of the jars containing the bacteria, you quickly calculate that the jar will be full at 10:00AM. When is
the jar be 1/3 full? _________________ How many bacteria (in exponential notation) are in the jar at this
time? ______________
4.
One of the bacteria is a sophisticated math-genius and also recognizes the problem. When the jar is full, their
world will come to an end in the next moment. She gets on her soapbox and exclaims “The end of the world is
just 6 minutes away!” What time is this? _____ Bacteria count:_______ She convinces the colony to start a
space-exploration mission to find new worlds. Two space rockets go out and return within 2 minutes to safely
2
evacuate 3 of the current population before they triple again. These two carriers have successfully located 2
new worlds that are each triple the size of the original world. What is the current population in each of these
three worlds? (Hint: population is a function of time)
5.
How much time does the remaining population in the original jar have left after the evacuations?
6.
How much time has each of the “new worlds” gained for themselves?
State the population of each of these: _________
7.
Chemistry pH: In chemistry, the pH of a liquid is a measure of its acidity. We calculate pH with:
pH = -log[H+] where H+ is the hydrogen ion concentration in moles per liter.
a. The Hydrogen concentration of human blood is normally about 3.98 x 10-4 moles per liter. Find the pH.
b. The Hydrogen concentration of fresh brewed coffee is about 1.3 x 10-5 moles per liter. Find the pH.
8.
Very fun challenge Log problem.
Find the sum:
1
2
3
4
98
99
Log (2)+ Log (3)+ Log (4)+ Log (5)+…….+ Log (99)+ Log (100)
Note you will need to use the property: LogaMN = LogaM + LogaN
9.
Using P(t) = P0ekt, suppose that $5000 is invested in a savings account where interest is compounded
continuously at 2.5% per year.
a. What is the balance after 1 year? 2 years?
b. When will the original investment double?