Question

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.

Answer #1

This problem is actually no different than one for interest on a bank account. 5% relative growth means that each year has 5% higher population than the previous year. The general equation is:

P_{f} = P_{i}(1 + r)^{t} where
P_{f} is the final population, P_{i} is the initial
population, r is the annual growth rate in decimal (not %), and t
is the time in years.

A) P_{f} = 23600(1.05)^{t}

B) P_{f} = 23600(1.04)^{8} =
32298.23

Round to the nearest integer = 32298 fox in 2008

**Hope This Helps!**

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...

The bear population in a certain region has been declining at a
continuous rate of 5% per year. In 2012
there were 764 bears counted in the area.
a) Write a function f(t) that models the number of bears
t years after 2012.
b) What is the population of bears predicted to be in 2020?

Requirement 1a.
A.
In 2000, the population of a country was approximately 5.63
million and by 2060 it is projected to grow to
11 million. Use the exponential growth model
A=A0 ekt
in which t is the number of years after 2000 and A0
is in millions, to find an exponential growth function that models
the data.
B.
By which year will the population be 7 million?
Requirement 1b.
The exponential models describe the population of
the indicated country, A,...

The number of bacteria in a certain population increases
according to a continuous exponential growth model, with a
growth rate parameter of
2.3% per hour. How many hours does it take for the
size of the sample to double?

The population of a region is growing exponentially. There were
35 million people in 1980 (when t=0) and 70 million people in
1990.
Find an exponential model for the population (in millions of
people) at any time t, in years after 1980. P(t)=
What population do you predict for the year 2000? Predicted
population in the year 2000 = million people.
What is the doubling time? Doubling time = years.

The population of a region is growing exponentially. There were
20 million people in 1980 (when t=0) and 70 million people in 1990.
Find an exponential model for the population (in millions of
people) at any time tt, in years after 1980.
P(t)=
What population do you predict for the year 2000?
Predicted population in the year 2000 = million people.
What is the doubling time?
Doubling time = years.

Suppose that nominal wage growth is 5 percent per year and the
inflation rate( the growth of aggregate prices) is 2% per year, the
growth of the real wage rate is
A 10 percent per year
B -3 percent per year
C 3 percent per year
D 7 percent per year

An evergreen nursery usually sells a certain shrub after 5 years
of growth and shaping. The growth rate during those 5 years is
approximated by
dh/dt =
1.7t + 8, where t is the time (in years)
and h is the height (in centimeters). The seedlings are 10
centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) = _____
(b) How tall are the shrubs when they are sold?
___ cm

The population of the world in 1975 was 15 billion and the
relative growth rate was estimated at 0.15 percent per year.
Assuming that the world population follows an exponential growth
model, find the projected world population in 2018.

The population of the world in 1990 was 50 billion and the
relative growth rate was estimated at 0.5 percent per year.
Assuming that the world population follows an exponential growth
model, find the projected world population in 2018.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 21 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 33 minutes ago

asked 43 minutes ago

asked 44 minutes ago

asked 52 minutes ago