The population P of a small town grows according to the function P1t2= 100 e t>50, where t is the number of years after 2010. How long does it take the population to double?

Q: Q4:- Construct the following mathematical models :- 1) The time rate of change of a population P is…

A: See the attachment

Q: The wolf population on Isle Royale, t years after 16 wolves are introduced, is modelled by the…

A: given, P= 16 e0.03t at t = 15 years P = 16 e0.03*15 =25.09

Q: The doubling period of a bacterial population is 1515 minutes. At time t=120t=120 minutes, the…

A: The doubling period of a bacterial population is 15 minutes. Let the initial population be P0. Then…

Q: f(t : = 500e0.05t Consider a bacterial population that grows according to the function measured in…

A:

Q: 4) How quickly is an airplane's elevation currently rising if its height (in feet) as a function of…

A: We need to find rate of change of elevation or rate of change of height when t = 4 sec Hence we will…

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A: In the question it is asked to calculate instantaneous velocity of the rocket at the instant when…

Q: NASA launches a rocket at t=0t=0 seconds. Its height, in meters above sea-level, as a function of…

A: Given information: The height function is ht=-4.9t2+355t+304. Calculation: The rocket will splash…

Q: An object is propelled vertically upward with initial velocity of 20 meters per second. The distance…

A:

Q: 1. Consider a population of bacteria that grows according to the function P(t) = 700e0.85, where t…

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Q: b) Consider a Population of bacteria that grow according to the function f(t) = 400e°.04t where t is…

A:

Q: A particular radioactive isotope has a half-life of 400 years. The time required for only A% of the…

A: The half-life of the radioactive element is the time during which half of the radioactive element…

Q: The number of bacteria in a culture is modelled by the function n(t) = 500 e 0.45t, where t is…

A:

Q: 5. The temperature of air in a room in Degrees Fahrenheit is represented by the function t(x) =…

A: Temperature in degree Fahrenheit is given by the equation  t(x)  =  8x + 21   x is the number of…

Q: To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500…

A: a) Given that, the function is Ct=40t160+t. Substitute Ct=15gL in Ct=40t160+t,…

Q: The value of a timber forest after t years is given by V (t) = 480√ t − 80t. After how many years is…

A: Topic-application of derivative

Q: A 2,916-liter cistern is empty when water begins flowing into it (at t=0) at a rate (in L/min) given…

A:

Q: The population of a city is P(t) = 2 · e0.06t (in millions), where t is measured in years. Calculate…

A: Given,               P(t)=2.e0.06t(in millions),The doubling time for exponential growth and the…

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 35e0.012,…

A:

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 40e0.8t,…

A: Given that rate of growth of sales for a particular company is 40e0.8t  initial sale , s=300 , t=0To…

Q: The number of applications for patents, N. grew dramatically in recent years, with growth averaging…

A:

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

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Q: In 2003 the number of online viewers was projected to grow according to the function. N(t)= 52t0.531…

A: As t=1 corresponds to 2003 then the value of t corresponds to 2010 is 2010-2003+1=8 Put this t=8…

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A:

Q: The number of bacteria in a culture is given by the function n(t) = 925e0.5t where t is measured in…

A: The number of bacteria of culture is given by the functionnT=925e0.5 twhere t is measured in hours…

Q: The population of a city is growing at a rate of 7.2% per year according to the formula P(t)=12000…

A: Given,  The population growth formulaP(t) =12000e0.072t and rate of growth r = 7.2%we have to find…

Q: The doubling period of a bacterial population is 1515 minutes. At time t=90t=90 minutes, the…

A: Given: The doubling period of a bacterial population is 15 minute. At time t = 90 minutes, the…

Q: How long will it take is sample of radioactive substance to decay to half of its original amount, if…

A: Find the time t.

Q: A population of bacteria is growing according to the equation P(t) = 300e0.17t , where t is the…

A:

Q: The percentage of residents of a certain country who use the Internet can be approximated by the…

A: We are given with the function which gives the percentage of residents using internet service at a…

Q: 5. Consider the population of bacteria grows according to the function f(t) 200e0.02t, where t is…

A: The solution of the problem is given in the next steps.

Q: If a rock is thrown upward on the moon with a velocity of 15 m/s, its height (in meters) after t…

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Q: NASA launches a rocket at t=0t=0 seconds. Its height, in meters above sea level, as a function of…

A:

Q: A population of bacteria is growing according to the equation P(t) = 750e0.21t , where t is the…

A:

Q: Suppose you are going hiking and over the course of your trip, your velocity at time t hours is…

A: The time t is from 0 to 4 Because initial time = 0 hour after 4 hours, t=4

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A:

Q: A startup business projects its instantaneous rate of revenue flow to be given by R(x)=120,000e^.03t…

A:

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A: Rt=10t5t2+4

Q: The doubling period of a bacterial population is 1010 minutes. At time t=100t=100 minutes, the…

A: The bacterial population count be p for n growth cycles we have 2np count of population cycle is…

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A: Total amount of pollutant dumped is obtained by integrating the function A(t)

Q: The rate of change of the income produced by a business selling face shields is given by f(t) =…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

Q: The population of a slowly growing bacterial colony after t hours is given by p(f) = 4t² + 30t +…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The doubling period of a bacterial population is 1010 minutes. At time t=90t=90 minutes, the…

A:

Q: The number of bacteria in a culture is given by the function n(t) = 955eº. where t is measured in…

A: It is given that the number of bacteria in a culture is given by the function n(t)=955e0.5t where t…

Q: The doubling period of a bacterial population is 2020 minutes. At time t=110t=110 minutes, the…

A:

Q: At 2:00 PM a car's speedometer reads 50 mi/h. At 2:15 PM it reads 75 mi/h. Show that between 2:00…

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Q: A population of bacteria is growing according to the equation P(t) = 550e0.0st , where t is the…

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Q: The rate at which blood pressure decreases in the aorta of a normal adult after a hearbeat is dp/dt=…

A: It is given that rate at which the blood pressure decreases in the normal adult is…

Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

A:

Q: A ball is thrown vertically upward. After t seconds, the height h (in feet) of the ball is given by…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.