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3. a) On Lonely Island, 100 rabbits are let loose. The population of rabbits grows proportional to the population size. After 2 months, there are 900 rabbits. How long will it take for the population to reach 2700 rabbits? 4 marks) 2-In(t1)2 b) On Lonely Island, there are also snakes. The snake population can be modelled by Pt)41 where t is measured in months. What is the average number of snakes during the first 2 months? Answer with an exact...
In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000 + 8000+?. dP a) Find the growth rate dt b) Find the population after 10 yr. c) Find the growth rate at t= 10. d) Explain the meaning of the answer to part (c).
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
The population P of a city grows exponentially according to the function P(t) = 8000(1.2) Osts where t is measured in years. (a) Find the population at time <= 0 and at time <= 2. (Round your answers to the nearest whole number.) PCO) P(2) - (b) When, to the nearest year, will the population reach 16,000? yr
QUESTION 2 A population P(t) (where t is the time in years) undergoes yearly seasonal fluctuations such that the rate of population growth is proportional to a fraction rP(t) of the total population, where r = cos 2rt Initially, the population is P After 3 months (1e 3/12 years), the population grows to 110% of its imitial sıze maximum value that P(t) can attain? At what tıme(s) does P(t) attan its maxımum? What is the [12] QUESTION 2 A population...
A population numbers 14,000 organisms initially and grows by 8.8% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a.b' where P = If 24500 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent. (a) Annual: $...
(1 point) A culture of yeast grows at a rate proportional to its size. If the initial population is 80008000 cells and it doubles after 33 hours, answer the following questions.1. Write an expression for the number of yeast cells after tt hours.Answer: P(t)=P(t)= 2. Find the number of yeast cells after 77 hours.Answer: 3. Find the rate at which the population of yeast cells is increasing at 77 hours.Answer (in cells per hour):
Suppose the population grows (in thousands) according to the following relationship, P=125e0.012t , where t is the number of years. Using logarithms, find the number of years t, it would take for the population P, to double, that is equal 250. Also comment on the meaning of the exponent
21² + 6 Ay The population, P, in thousands of a resort community is given 100 600t by P(t) = t20, where t is time, in months. 80-A a) Find the population at t= 0, 1, 3, and 8 months. .60 b) Find the horizontal asymptote of the graph and determine the 401 value that P(t) approaches as t goes to co? c) Explain the meaning of the answer to part (b) in terms of the 20- application 0 10...
*10. The size P of a certain insect population at time t (in days) obeys the function P(t) = 100 e 0.04 (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 140? (e) When will the insect population double? (a) What is the number of insects at t= 0 days? insects (b) What is the...