Question

A certain woodrat population went from 100 to 110 in one year. Suppose population growth rate continues in this exponential way. Calculate R? b) Calculate r? c) What will the population be 10 years after the original N = 100? d) What is the expected doubling time for this population?

Answer #1

Suppose that a population of deer is experiencing exponential
growth, with r= 1.5 individuals/year. If the population size now is
4, how many deer will be added to the population in the next year?
If necessary, truncate your answer to a whole number. Show your
work.
Suppose that a population of deer is experiencing exponential
growth, with r= 0.89 individuals/year. If the starting population
size was 8, how many deer will be in the population after 5 years?
If necessary,...

Complete the following table.
Population
Growth Rate, k
Doubling Time, T
Country A
2.4
%
per year
Country B
24
years
Population
Growth Rate, k
Doubling Time, T
Country A
2.4
%
per year
nothing
years
Country B
nothing
%
per year
24
years

1) a) The fox population in a certain region experiences
exponential growth with a relative growth rate of 8% a year. In
2013, it was estimated that the population was 18, 000. (a) Find a
function that models the population t years after 2013. (b) Use the
function above to estimate the fox population in the year 2021. (c)
After how many years will the fox population reach 25, 000?
b) Two observers simultaneously measure the angle of elevation of...

city begins with population of P_0 = 50,000 and has a growth
rate of r = 15%
a) Find R and give the recursive formula. Use this to find P_1
and P_2
b) Give the explicit formula for P_N. What is P_11?
c) (bonus) find the time until the population reaches 950,000
(or more)
Exponential sequence explicit formula
, R = common ratio, r = growth rate
{ P_N = P_0 R^N, where R = 1+r is the common ratio,...

1. A population grows according to an exponential growth model.
The initial population is P0=12, and the common ratio is
r=1.45
Then:
P1 =
P2 =
Find an explicit formula for Pn. Your formula should
involve n.
Pn =
Use your formula to find P9
P9=
Give all answers accurate to at least one decimal place
2. Assume there is a certain population of fish in a pond whose
growth is described by the logistic equation. It is estimated that...

With exponential growth rates we often calculate “doubling
times.” Hypothetically, if the world’s human population was growing
exponentially and doubling every 60 years, and you were told all
the areas suitable for humans would be fully
occupied by the year 2100, what
year would the world’s human habitats be HALF
occupied

3.) Starting with the expression for logistic population growth,
determine the expression for the time t1 that it takes for
population to grow from No to N1. Express your answer in terms of
four variables only: r, K, No, and N1.
4.)The rate of growth of a population is given by dN/dt = 100t.
If the total population at t = 10 years is 6000 people, find the
population at t = 20 years. This distribution is NOT exponential or...

Suppose that the growth rate of the population of city X is
proportional to the population of X. We have the following data:
the population in 1945 was 36,000 and the population in 1990 was
63,000. Establish and solve an Initial Value Problem to express the
population of X as a function of time, graph this function and
calculate an estimate of the population in the year 2040.

The fox population in a certain region has a continuous growth
rate of 5 percent per year. It is estimated that the population in
the year 2000 was 23600. (a) Find a function that models the
population t years after 2000 (t=0 for 2000) (b) Use the function
from part (a) to estimate the fox population in the year 2008.

Suppose we have a whale population that has been declines to
1000 individuals. The growth rate is 2% a year and the carrying
capacity is 10,000. Calculate (use Excel) how many years are needed
to have the population recover to 5,000 or more, meaning that
during those years, no harvesting can take place. Once the
population is recovered, how many whales can be harvested per year
in a sustainable way?

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