A study of air quality in a particular city by an environment group suggests that t years from now, the level of carbon mnoxide, in parts per million, in the air can be modeled by the function A(t)=0.2t²+0.1t+5.1. What will the level be (in parts per million) three years from now? How many years from now will the level of carbon monoxide be at 8 parts per million? Round to the nearest tenth hundredth.

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

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

A: Consider the function that models the number Pt=Aekt=B2tC Here, the objective is to find the…

Q: the number of bacteria in a culture was initially 8,000 and the number grew to 12,000 in 6 hours.…

A:

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A:

Q: 3. The number of students infected with flu at Springfield High School after t days is modeled by…

A:

Q: The deeper you are under water; the less sunlight reaches you. The percent of sunlight, P, that…

A: We will modern the following question by the function in next step.

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: A climatologist is measuring glacial run-off during the weeks before winter sets in again and the…

A: Given, rt = 60t2+3-20e1-2t  Where t is the number of weeks since measurements began and rt is the…

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: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: The air in a room with volume 180 m3 contains 0.15% carbondioxide initially. Fresher air with only…

A:

Q: The population of a bacteria culture was 2000 at 6 AM and was increasing at a rate of 10% per hour.…

A: The increase in the rate of bacteria  population can be given by the function

Q: The population of Egypt can be modeled by the function P(t) = 114(1 + 0.018) where P(t) measures the…

A: topic - exponential function

Q: A toy rocket is shot vertically into the air from a 4​-foot-tall launching pad with an initial…

A: Initial height = 4 foot initial velocity = 168 feet/sec The height of the rocket in feet t seconds…

Q: . The population of the state of Georgia (in thousands) from 1995 (1 = 0) is modeled by the function…

A: NOTE: Refresh your page if you can't see any equations. . for the year 2000, take t=5…

Q: The magazine Scientific American released a study of data analysis on how quickly children are able…

A: The function P(t) represents the percentage of children who can speak in at least single words by…

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

A:

Q: new

A: Please refer to the image below

Q: The function P =f(n) = 45127(0. 943)“ models the anticipated population, P, of a small town in…

A: Given, P=fn = 451270.943n  Where P is the population of the town and n represent the number of years…

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

A:

Q: 4. Jan invested $2500 in an investment vehicle that is guaranteed to earn 4% interest compounded…

A: The given account equation is A(t)=2500(1.04)t. (a) Evaluate the value of A0 and A10. (b) What do…

Q: The half-life of chemical substance is approximately 9 years. Initially there is 80 grams of the…

A:

Q: The population of a pod of bottlenose dolphins is modeled by the function A ( t) 8(2)t , where t is…

A:

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

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: An experimental drug was injected into the bloodstream of a rat. The concentration C(t) of the drug…

A:

Q: The Montag Family purchased a house in 2020 and expects its value (in thousands of dollars) t years…

A: Here, modeled function  V(t)=310(1.08)t    Which means initially price of the house is 310 thousands…

Q: The population of rabbits on an island is modeled by the function P (t) = Poekt 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…

A:

Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

A:

Q: For each year, the population of a forest of trees is represented by A(t)=115(1.025)t.   In a…

A:

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A:

Q: A7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min) given…

A: The given capacity of cistern is is 7986 litre

Q: 7 Since the development of the iPod, the stock price of Apple has been growing rapidly and has been…

A: Given that the stock price of Apple has been growing rapidly using equation y=3.2e0.5x We compare…

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: A 8,000-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A: Given the function for rate of water flowing is, Here t is measured in minutes. a. Given the time…

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: 4. At Wally Motors, an auto engineer, in testing a new engine on one of its new models, found that…

A:

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

A:

Q: A 7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A:

Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

Q: The number of bacteria in a culture is given by the function n(t)=950e^0.35t where t is measured…

A: The number of bacteria in a culture is given by n(t) = 950e^{0.45t}e0.45t

Q: Following an unexplained decline in the number of birds of prey on his property, a farmer sees a…

A: The function Mt=3001.4t can be used to estimate the number of small mammals on the premises within t…

Q: A geologist is using stratigraphy to analyze the history of a canyon wall overlooking a river, in a…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: the value of an investment is modelled by A(t)=5000e0.09t , where A is the amount the investment in…

A:

Q: The city of San Estaban had a population of 45,000 in 2015 (t=0) and was growing continuously at an…

A:

Q: A drug is injected into the body in such a way that the concentration, C, in the blood at time t…

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.