Modeling with Exponential and Logarithmic Functions

5. A bacteria culture grows by the exponential model y = 200e kt . How many bacteria
are there initially If the number of bacteria triples in 2 hours, find the number of
bacteria after 5 hours.
6. A bacteria culture starts with 600 bacteria and grows by the exponential model
y = y 0 e kt . After 3 hours there are 2400 bacteria. Find the number of bacteria after
4 hours. When will the number of bacteria be 5000
7. Suppose that a population grows by 3% per year. Find the time it would take for
the population to double.
8. Suppose that a population grows by 5% per year. Find the time it would take for
the population to triple.
9. Happyville and Smileytown both have a population of 10,000 people presently. Happyville
is increasing by 1500 people a year and Smileytown is increasing by 15% a
year.
a) Which town is growing faster
b) Find formulas for the populations of these towns as function of time t in years.
c) Use part b) to predict the size of both towns 5 years from now.
d) Find a year in which population of Happyville will be over 25000. Do the same
for Smileytown.
10. The half-life of bismuth 210 is 5 days. How many days it will take the 1.5 grams of
bismuth 210 to decay to 0.3 grams
11. The biological half-life of triazolam, a drug used for treating insomnia, is 2.3 hours.
What percent of an initial dose will remain after 5 hours
12. The table below shows the number of rabbits in a local forest from 1982 to 1996.
year 1982 1985 1988 1991 1994 1996
number of rabbits 20 67 139 182 196 198
Find a logistic model to fit this data. In what year were there 99 rabbits
13. The table below shows the concentration of a drug in a patients bloodstream t hours
after it was administered.
time (hours) 0 1 2 3 4 5
concentration (mg/cc) 2.5 2.29 2.1 1.95 1.81 1.7
Find the exponential model that fit this data. When will the concentration drop
bellow 1.2 mg/cc
14. A new drug was put on the market in 1990. The table below shows the number of
prescriptions written for this drug over a 10 year period.
year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
numb. of prescr. 142 149 154 155 159 161 163 164 164 166
Find a logarithmic model for this data. Using the model, how many prescriptions
will be written in 2006 In what year will there be 178 prescriptions