Question

A population of insects currently numbers 22,800 and is increasing at a rate of R(t) = 1225e^0.14t insects/week. If the survival function for the insects is S(t) = e^−0.2t, where t is measured in weeks, how many insects are there after 12 weeks?

Answer #1

An animal population currently has 7400 members and is
reproducing at the rate R(t) = 2290 + 40t members/year. The
proportion of members that survive after t years is given by S(t) =
1/(t + 1)
(a) How many of the original members survive 4 years?
(b) How many new members are added during the next 4 years?
(c) Explain why the animal population 4 years from now is not
the same as the sum of your answers from parts...

A radioactive material disintegrates at a rate proportional to
the amount currently present. If Q(t) is the amount present at time
t, then
dQ/dt =−rQ
where r>0 is the decay rate.
If 100 mg of a mystery substance decays to 81.14 mg in 4 weeks,
find the time required for the substance to decay to one-half its
original amount. Round the answer to 3 decimal places.
______________weeks

The per capita growth rate of many species varies temporally for
a variety of reasons, including seasonality and habitat
destruction. Suppose n(t) represents the population size at time
t, where n is measured in individuals and
t is measured in years. Solve the following differential
equation.
Habitat destruction is modeled as
n' = (r − at)n n(0) =
n0.
Here the per capita growth rate declines over time, going from
positive to negative. It is modeled by the function r −...

The traffic flow rate (cars per hour) across an intersection is
r ( t ) = 500 + 800 t − 180 t^2 , where t is in hours, and t =0 is
6am. How many cars pass through the intersection between 6 am and
10 am?

The growth rate of a colony of ants is given by the
formula
10t(1+t2)2
where t is measured in hours. If 100
ants are initially present then how many are present after 2
hours?
The number of ants present after 2
hours is _________.

Consider a project to produce custom door moldings for GMC
Acadia cross-over vehicles, described in the following table.
Activity Activity Time (weeks) Immediate
Predecessor(s)
START 0 -
A 2 START
B 6 START
C 1 B
D 2 A
E 8 A, B
F 8 D, E
G 2 C, E
FINISH 0 F, G
You are interested in completing your project as soon as
possible. You have only one option. Suppose you could assign
Employee A, currently assigned to...

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...

A magazine currently has 8400 subscribers for its online web
version. It is adding members at the rate of R(t) = 140e0.03t
subscribers per month. If the proportion of members who remain
subscribed t months from now is S(t) = e−0.06t, how many online
subscribers will the magazine have three years from now?
(Round your answer to the nearest integer.) subscribers

The number of Drosophila fruit flies in a controlled experiment
assumes the following growth pattern when the food source is
limited:
N(t)=6501+12e−0.3tN(t)=6501+12e−0.3t
where tt measured in days.
A. How many fruit files were there in the beginning?
equation editor
B. What is the limiting number of fruit flies?
equation editor
C. At what time was the population increasing most rapidly?
equation editor
D. At what rate is the number of fruit flies increasing after 5
days?
equation editor

1- A spherical balloon is inflated so that its volume is
increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the
diameter of the balloon increasing when the diameter is 1.5 feet?
The diameter is increasing at ft/min.
2- A 16 foot ladder is leaning against a wall. If the top slips
down the wall at a rate of 3 ft/s, how fast will the foot be moving
away from the wall when the top is 12 feet above the...

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