Methylmercury is a toxic compound that can lead to neurological problems and an increased risk of heart disease. It takes about 50 days for the human body to eliminate 50 % of a given quantity of the compound from the system. Suppose a test shows that there are 600 micrograms of methylmercury in a person’s body and that y t is the number of micrograms present t days later. Assume that y t has as an exponential decay model with a half-life of 50 days and that no additional methylmercury is absorbed from the environment. (a) Find an initial-value problem whose solution is y t . (b) Find a formula for y t . (c) How many milligrams will be present after 4 weeks? (d) How long will it take for 70 % of the methylmercury to be eliminated from the person’s body?
Methylmercury is a toxic compound that can lead to neurological problems and an increased risk of heart disease. It takes about 50 days for the human body to eliminate 50 % of a given quantity of the compound from the system. Suppose a test shows that there are 600 micrograms of methylmercury in a person’s body and that y t is the number of micrograms present t days later. Assume that y t has as an exponential decay model with a half-life of 50 days and that no additional methylmercury is absorbed from the environment. (a) Find an initial-value problem whose solution is y t . (b) Find a formula for y t . (c) How many milligrams will be present after 4 weeks? (d) How long will it take for 70 % of the methylmercury to be eliminated from the person’s body?
Methylmercury is a toxic compound that can lead to neurological problems and an increased risk of heart disease. It takes about 50 days for the human body to eliminate
50
%
of a given quantity of the compound from the system. Suppose a test shows that there are 600 micrograms of methylmercury in a person’s body and that
y
t
is the number of micrograms present t days later. Assume that
y
t
has as an exponential decay model with a half-life of 50 days and that no additional methylmercury is absorbed from the environment.
(a) Find an initial-value problem whose solution is
y
t
.
(b) Find a formula for
y
t
.
(c) How many milligrams will be present after 4 weeks?
(d) How long will it take for
70
%
of the methylmercury to be eliminated from the person’s body?
Tuberculosis (TB) is one of the top 10 causes of death worldwide. According to the World Health Organization (WHO), deaths from TB have fallen by an average of 1.2% per year between 2000 and 2015. In the year 2000, there were approximately 2.5 million deaths from TB.
Part 1. Use the given data to create an exponential decay function to model the number of deaths from TB in terms of years, tt, where t=0 represents the year 2000.
Part 2. Use this function to determine the year in which the number of deaths from TB was 2.1 million.
The mean life of a radioactive material is the reciprocal of its decay constant. Show that 95% of a radioactive material decays approximately in a time period of 3 times its mean life.
In 1991 it was estimated that there were about 100 breeding pairs of Northern Spotted Owls. It was determined that their population had been
declining at a rate of 7% each year. If 'P' is the population of the owls, write the equation that would model the population of the Northern
Spotted Owl after t years.
O A.P = 100 (93)*
O B. P = 100 (7%)'
OC.P= 100 (1.7)*
OD. P = 100 (7)
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