“When are we ever going to need this”
Exponential Equations
Fighting the Flu
A biologist just discovered a new strain of bacteria that helps defend the human body against
the flu virus. To know the dosage that should be given to someone, the doctor must first know if
the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria
multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are
now 12 cells in the dish.
Complete the table to show ​
C(h) ​
the number of cells that will be in the dish after ​
h​
hours. Then
plot the points on the graph below. (Round to the nearest whole cell)
h
0
1
C(h)
10
12
2
3
4
5
6
7
8
9
10
11
12
13
14
15
154
Use the pattern you used to fill in the table to write a function ​
C(h)​
to represent the number of cells after ​
h​
hours.
C(h)​
=
Graph ​
C(h) ​
in your calculator (don’t forget to adjust the window) and compare it to the data you plotted. Does the
graph match the data?
Use the function to find the number of cells present after a full day. Round to the nearest cell.
If it takes 1,750 cells to make an effective dosage, about how many hours will it take to make a dosage starting with
10 cells?
How does the equation change if the biologist starts with 75 cells? What would the new equation be? How would that
change the graph?
How long would it take to make a complete dosage if the biologist starts with 75 cells?
“When are we ever going to need this”
Exponential Equations
Carbon Dating
When a plant or animal dies, it stops acquiring carbon­14 from the atmosphere. Carbon­14
decays over time with a half­life of about 5,730 years. That is, about half the amount of
carbon­14 that was in the live plant or animal remains present 5,730 years after it has died.
The percent ​
P​
of the original amount of carbon­14 that remains in a sample after ​
t​
years is
given by this equation:
P = 100( 12 ) t/5730
What percent of the original carbon­14 remains in a sample after:
● 2,500 years?
●
5,000 years?
●
10,000 years?
Pick 3 other years to calculate the percent. Then graph the model. Label both axes.
An archaeologist found a bison bone that contained about 37% of the carbon­14 found in the same bone of a live
bison. Use the graph to estimate the how long ago the bison died..
What does the y­intercept of the graph represent in this problem?
How many years does it take for the carbon­14 to completely disappear from a specimen?
What similarities and differences are there between the graphs and/or equations in this problem and the bacteria
problem?
“When are we ever going to need this”
Exponential Equations
Fighting the Flu (​
Key)
A biologist just discovered a new strain of bacteria that helps defend the human body against
the flu virus. To know the dosage that should be given to someone, the doctor must first know if
the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria
multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are
now 12 cells in the dish.
Complete the table to show ​
C(h) ​
the number of cells that will be in the dish after ​
h​
hours. Then
plot the points on the graph below. (Round to the nearest whole cell)
h
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
C(h)
10
12
14
17
21
25
30
36
43
52
62
74
89
107
128
154
Use the pattern you used to fill in the table to write a function ​
C(h)​
to represent the number of cells after ​
h​
hours.
C(h)​
= 10 * 1.2h
Graph ​
C(h) ​
in your calculator (don’t forget to adjust the window) and compare it to the data you plotted. Does the
graph match the data? ​
Hopefully!
Use the function to find the number of cells present after a full day. Round to the nearest cell.
10 * 1.224 = 795cells
If it takes 1,750 cells to make an effective dosage, about how many hours will it take to make a dosage starting with
10 cells?
About 28 hours
How does the equation change if the biologist starts with 75 cells? What would the new equation be? How does that
change the graph?
C(h) = 75 * 1.2h ; the graph would shift up so that the new y­intercept is 75 instead of 10.
How long would it take to make a complete dosage if the biologist starts with 75 cells?
About 17 hours
“When are we ever going to need this”
Exponential Equations
Carbon Dating
When a plant or animal dies, it stops acquiring carbon­14 from the atmosphere. Carbon­14
decays over time with a half­life of about 5,730 years. That is, about half the amount of
carbon­14 that was in the live plant or animal remains present 5,730 years after it has died.
The percent ​
P​
of the original amount of carbon­14 that remains in a sample after ​
t​
years is
given by this equation:
P = 100( 12 ) t/5730
What percent of the original carbon­14 remains in a sample after:
● 2,500 years? ​
73.9%
●
5,000 years? ​
54.6%
●
10,000 years? ​
29.8%
Pick 3 other years to calculate the percent. Then graph the model. Label both axes.
Points will vary
An archaeologist found a bison bone that contained about 37% of the carbon­14 found in the same bone of a live
bison. Use the graph to estimate the how long ago the bison died..
About 8,200 years
What does the y­intercept of the graph represent in this problem?
100%, the amount of carbon­14 present at the time the specimen dies
How many years does it take for the carbon­14 to completely disappear from a specimen?
It will never completely disappear, it will just keep decreasing in amount forever
What similarities and differences are there between the graphs and/or equations in this problem and the bacteria
problem?
Answers will vary;
This graph is decreasing, the other is increasing.
Both equations include a variable in the exponent.
The base in this equation is less than 1, the base in the other is greater than 1.
“When are we ever going to need this”
Exponential Equations
To edit this worksheet or answer key in Google Docs, use the link below:
https://docs.google.com/document/d/1tJyxLRMSG3iqStDkv­Wz0Mrocuo8_BohPYKAtG93W1A/pub