Question

A population of insects increases at a rate of 240+12t+0.3t^2
insects per day. Find the insect population after 5 days, assuming
that there are 70 insects t=0.

Answer #1

The size P of a certain insect population at time t (in days)
obeys the function
P(t)=600e0.06t.
(a) Determine the number of insects at
t=0 days.
(b) What is the growth rate of the insect
population?
(c) What is the population after 10 days?
(d) When will the insect population reach
720?
(e) When will the insect population
double?

The size P of a certain insect population at time t (in days)
obeys the function P(t)=100e^0.07t
(a) Determine the number of insects at t=0 days.
(b) What is the growth rate of the insect population?
(c) What is the population after 10 days?
(d) When will the insect population reach 120?
(e) When will the insect population double?

The population P of bees in a certain area increases
at a rate proportional to the current population with the
proportionality constant 5. There are 25000 bees in the area
initially, and birds eat 2500 bees per day. Determine the
population of bees in the area after 37 days.

The population of mosquitoes in a certain area increases at a
rate proportional to the current population, and in the absence of
other factors, the population doubles each week. There are 200,000
mosquitoes in the area initially, and predators (birds, bats, and
so forth) eat 50,000 mosquitoes/day. Determine the population of
mosquitoes in the area at any time. (Note that the variable
represents days.)
Correct answer :
200000*e^(ln(2)/7*t)-350000/ln(2)*(e^(ln(2)/7*t)-1)

The rate of growth of sales (sales per day) for a particular
company is predicted to be 45e^0.04t , beginning with
sales of 300 items on day t = 0.
Find a formula for the total number of sales in the first
t days.

The population of mosquitoes in a certain area increases at a
rate proportional to the current population, and in the absence of
other factors, the population doubles each week. There are 800,000
mosquitoes in the area initially, and predators (birds, bats, and
so forth) eat 60,000 mosquitoes/day. Determine the population of
mosquitoes in the area at any time. (Note that the variable t
represents days.)

The population of mosquitoes in a certain area increases at a
rate proportional to the current population, and in the absence of
other factors, the population doubles each week. There are 700,000
mosquitoes in the area initially, and predators (birds, bats, and
so forth) eat 60,000 mosquitoes/day. Determine the population of
mosquitoes in the area at any time. (Note that the variable t
represents days.)

The population P(t) of
mosquito larvae growing in a tree hole increases according to the
logistic equation with growth constant k = 0.3
days−1 and carrying capacity A = 800. Find a
formula for the larvae population
P(t), assuming an initial
population of P(0) = 80 larvae.
P(t) =______________

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.

The population of a bacterial culture develops with constant
relative growth rate of 0.9758 per member per day. Initially the
population was one member. Determine the population size after 14
days.

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