suppose that a population is dying with a half life of of 43years. The initial size is 1600. Find the 1 year DTDS for this population
P(t)= 1600^(0.016t)
that is wrong
according to that equation. after one year the population would be 1.125.
THAT is not possible when the half llife is 43!!! afte 43 years the population would be 800.
To calculate the 1-year DTDS (Discrete Time Death and Survival) for a population, we need to consider the half-life and the initial size of the population.
The half-life of 43 years means that after every 43 years, the population will halve i.e., reduces by 50%. Since we want to find the 1-year DTDS, we need to determine how much the population changes year by year.
To calculate the 1-year DTDS, we can use the formula:
DTDS = (Population at t + 1 - Population at t) / Population at t
In this case, we will compare the population after 1 year (t + 1) with the initial population (t).
Let's calculate the 1-year DTDS for this population:
Population at t + 1 = Population at t - (Population at t * Growth rate)
Since the population is dying, the death rate is 50% (0.5) every 43 years.
Growth rate = -0.5
Population at t + 1 = Population at t - (Population at t * 0.5)
= 1600 - (1600 * 0.5)
= 1600 - 800
= 800
Now, let's calculate the 1-year DTDS:
DTDS = (Population at t + 1 - Population at t) / Population at t
= (800 - 1600) / 1600
= -800 / 1600
= -0.5
The 1-year DTDS for this population is -0.5 or -50%.
Please note that the negative sign indicates a decrease in the population.