The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the function --0.04t A(t) = 1, 600e where t represents the time in years from now. If the dumping continues unchecked, what will the total amount of pollutant dumped near the city? A tons TIP Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity

Q: In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was…

A: We need to find out the year in which the cost of mailing a first class letter reach 60 cents.

Q: The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is…

A: Given total cost ,                  (x)=-10x2+500x+110

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 number of bacteria P (h) in a certain population increases according to the following function,…

A: Here, the given function is: P(h)=1800e0.18h where h is the number of hours and P(h) is the number…

Q: The number of bacteria in a culture is given by the function ?(?) = 350?^0.8?, where t is measured…

A:

Q: Fifty percent of the amount of a certain drug is eliminated from the body every hour. A 500mg drug…

A: Given that, Fifty percent of the amount of a certain drug is eliminated from the body every hour…

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: Between 2006 and​ 2016, the number of applications for​ patents, N, grew by about 4.3​% per year.…

A: To solve the following problem

Q: Based on data for the years 1910-2007, the expected life span of people in Country A can be…

A: to find:- Birth year.

Q: The function ​f(x)=1300x-100x2 represents the rate of flow of money in dollars per year. Assume a…

A:

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given volume function fx=x3 to find instantaneous rate of change of the volume x=4 in

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

A: The given function for the revenue from sale of x no. of car seats for infants is R(x)=28x-0.010x2…

Q: Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: A culture of bacteria initially contains 153 cells and grows at a rate proportional to its size.…

A:

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

A:

Q: 1. Determine, to the nearest tenth, the instantaneous rate of change of the function f (x) = 4x³ –…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.9% per year. That…

A: Given: N'(t)=0.049 N(t)Therefore:dNdt=0.049 N

Q: A) The population of a country has grown at a rate proportional to the number of people in this…

A: Let the present population be P0 Then t years later the population is Pt and t years ago the…

Q: In 2000 the birthrate in a certain area increased from 18e0.02t million births per year to 23e0.02t…

A: Given that In 2000 the birthrate in a certain area increased from 18e0.02t million births per year…

Q: Between 2006 and 2016, the nurmber of applications for patents, N, grew by about 3.6% per year. That…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: An influenza virus is spreading through a school according to the function N = 9(1.17)* , where N is…

A: For a function, y=f(t), the independent variable is t and the dependent variable is y . The value of…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A:

Q: During a flu epidemic, the total number of students on a state university campus who had contracted…

A: "Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…

Q: Suppose that the population of some state in 2010 was P = 37 million and its annual percentage rate…

A:

Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

Q: The population of the United States is predicted to be P(t) = 310e0.0073t million, where t is the…

A:

Q: Please see photo attached

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: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.8% per year. That…

A: given: Between 2006 and 2016, the number of applications for patents N, grew by about 4.8 % per…

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That…

A: (a) N'(t)=0.041N(t)dNdt=0.041NdNN=0.041dt∫dNN=∫0.041dtln N=0.041t+celn…

Q: The annual amount of energy produced in a country from dry natural gas (in tnillion cubic feet) can…

A: Given function is gt=15.621.041t. Where t =10 represent year 2010. (a) Obtain the amount of dry…

Q: The length of a rectangle is increasing at a rate of 4 meters per day and the width is decreasing at…

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A:

Q: The number of banks in a country for the years 1935 through 2009 is given by the following function.…

A: The given function,f(x)=83.2x+12,362if x<90-376.3x+48,682if x≥90, where x is the number of years…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: Total money flows in 8 years=…

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

A:

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

A: R(x)=24x-0.010x20≤x≤2400 To find average change in revenue apply formula…

Q: g(t)=15.18(1.047)t​,

A: gt=15.181.047t The year 2010 corresponds to t=10.

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

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 3.1% per year. That…

A: Solve the differential equation by variable separation method. Use the initial condition to…

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

A:

Q: The country of Benin in West Africa has a population of 9.05 million people. The population is…

A: We use growth function.

Q: Find the intervals of increase and decrease  for the function.   f(x)= ln(lnx-4)

A: Simple increasing and decreasing problem.....

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: A company’s sales, in millions of peso, of electrical appliances can be modelled by S(x) = -1.3x3 +…

A: Step1 :         Given sales model by expression               S(x)=-1∙3x3+16x2+25∙4x+576     x is…

Q: According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million…

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: The average annual pay for truckers P in a certain country​ (in thousands of​ dollars) can be…

A:

Q: In 2010, the population of the United States was approximately 310 million with a 0.97% annual…

A: