M119 Chapter 4 –
Applications
- Since adding a new herbicide to
wheat seed, a farmer finds that the total yield of the crop can be modeled
by
where x represents the number of growing
seasons since the farmer started using the herbicide and f(x) represents the crop yield in
bushels.
a) Find 
b) Find and interpret 
- The average salary of players in
the National Basketball Association from 1983 to 1993 can be modeled by
where x represents the number of years
since January 1982 and f(x)
represents the average salary in thousands of dollars.
a) Classify the function as an
exponential growth or decay model.
Explain.
b) Find
c) Find and interpret 
and
.
- The tax liability of a since U.S.
resident with no dependents who earned at most $35,000 can be modeled by
where x represents the number of years
since January 1984 and f(x) represents
the tax liability in dollars.
a) Classify the function as an
exponential growth or decay model.
Explain.
b) Find
c) Find and interpret 
and
.
- A research assistant in biology
finds in an experiment that at low temperatures the growth of a certain
bacteria culture can be modeled by
, where t
represents the number of hours since the start of the experiment and f(t) represents the number of bacteria
present.
a) Determine 
b) Find and interpret 
and
.
- The city of
, where x
represents the number of years since the laws were adopted and P(x) represents the city’s
population.
a) Find 
b) Find and interpret 
and 
- Prescription drug companies have
found that the popularity of a certain drug has dwindled and can be
modeled by
, where x
represents the number of years that the drug has been on the market and f(x) represents the number of
prescriptions written for the drug annually in thousands.
a) Determine
b) Find and interpret 
and 
Solutions
1. a) 
b) The crop yield
will increase by approximately 476.33 bushels during the 6th growing
season
2. a)
growth b) 
c) f(3)=467 (In Jan. 1985 the salary was
$467,000), f’(3)=88.73 (during the
year 1985 the salary increased by approximately $88,730.)
3. a) decay
b) 
c) During the year 1987
the tax liability decreased by approx. $193.08.
4. a) 
b) f(12)
= 779 is the number of bacterial present 12 hours later, and f ’(1)=1 is the approx growth during the
next hour.
5. a) 
b) P(20)=10,299
the population 20 years after the laws were adopted,
P ‘(20) =5 is the approximate growth during
the next year.
6. a) 
, b) f(2)=153 (153,000
annual prescriptions were written when the drug had been on the market for two
years, f ‘(2)=2.5 (the number of prescriptions is growing at a rate of
2,500 per year)