Problem: The size P of a small herbivore
population at time t (in years) obeys the
function if they have
enough food and the predator population
stays constant. After how many years
will the population reach 1800?
Problem: The half-life of carbon 14 is 5600
years. A fossilized leaf contains 12% of
its normal amount of carbon 14. How
old is the fossil (to the nearest year)?
Newton’s Law of Cooling
•Temperature of a heated object decreases
exponentially toward temperature of
•Newton’s Law of Cooling
The temperature u of a heated object at a
given time t can be modeled by
where T is the constant temperature of the
surrounding medium, u0 is the initial
temperature of the heated object, and k is
a negative constant.
Problem: The temperature of a dead body
that has been cooling in a room set at
70°F is measured as 88°F. One hour
later, the body temperature is 87.5°F.
How long (to the nearest hour) before
the first measurement was the time of
death, assuming that body temperature
at the time of death was 98.6°F?
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