The population of the United States was 3.9 million in 1790 and 178 million in 1960. If the rate of growth is assumed proportional to the number present, a. find a function that describes the population of the United States in t year. b. calculate the estimated population in 2000 according to a.

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: An equipment currently worth $15,549 is expected to be worth $12,704 in 5 years. Assuming linear…

A: Here, given that the equipment is currently worth $15,549 and is expected to be worth $12,704 in 5…

Q: Is C(E), cost as a function of employee turnover, better modeled with a linear function or an…

A: Given data is: The point in the form of E,C

Q: The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is…

A: To find the maximum value, P''(I)<0. If this condition satisfies, then P will be maximum at I.

Q: The population of bison in Canada was found to have a growth rate of  20%. If the If the population…

A:

Q: As the water drains from a bathtub, the volume, V, in litres, of water remaining in the bathtub…

A:

Q: Which function will show the most rapid growth? OP = 1,000(0.905)* OP = 1,000(1.075)* OP=…

A: To find the function having maximum growth.

Q: let y=1200e0.11t When rewritten in the form y=ab^2, b= 1.11623  The annual growth rate or decay…

A: To find the annual growth rate or decay rate for this function as a percent

Q: Find the average rate of change of g(x) 5æ – 5 from x = - 3 to a = 3.

A:

Q: Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If  C'(10) =…

A: Given:C(t) is the cost of producing t tons of white paper.It is known that,

Q: A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the…

A:

Q: rate

A:

Q: The table shows the linear relationship between the average height in feet of trees on a tree farm…

A: Given that:

Q: A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount…

A:

Q: The population of a city doubles in 50 years. How many years will it be four times as much? Assume…

A: Given the population of a city doubles in 50 years. Given the rate of change is proportional to the…

Q: Which function has the greater rate of change? (b) How much greater is it?

A: The slope of function gives the rate of change function. The slope of equation passing through two…

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model…

A: Modeling a given set of data in 2 variables is the process of finding the expression relating the…

Q: The gross domestic product (GDP) of a certain country was N(t) = t² + 5t + 106 billion dollars t…

A: This is application of derivative so take the derivative and than put the value of time t.

Q: Suppose that the quantities whose values are represented s and r are related by a constant rate of…

A: Sol: Given     1) S T     2)   57.2     3) -10.7 12.9     4) 2.7 -45.7     5) 7.1…

Q: Use the fact that the world population was 2560 million in 1950 and 3040 million in 1960 to model…

A:

Q: If a new Mustang is valued at $20,000 and five years later it is valued at $8000 then what is the…

A: A new Mustang is valued at $20,000 and five years later it is valued at $8000. Let x be the year and…

Q: Consider the constant rate of decrease of a certain microorganism. At the start, there are 50000…

A: Given query is to find the population of microorganisms after 50 second.

Q: If up is measured as being positive, the height of a ball rising after being thrown has a rate of…

A:

Q: Given the function g(x) = -a² +5x +14, determine the average rate of change of the function over the…

A:

Q: A balloon is inflating at a constant rate of 9 cubic centimeters per second. When the volume of the…

A: Given: A balloon is inflating at a constant rate of 9 cubic centimeters per second. when the volume…

Q: The management of a large chain of frozen yogurt stores in New England believes that t days after…

A:

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We will find in how many year the population of country will be five times as shown below

Q: For the function ?(?) = ?2 − 2? + 5, estimate for the instantaneous rate of change at x = 3. Round…

A:

Q: A computer, using data from a refrigeration plant, estimated that in the event of a power failure…

A: The temperature in the freezer after t hours of power failure is given by, C=5t0.04t+1−35 To find…

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A:

Q: The population of country doubles in 100 years. How many years will it be five times as much? Assume…

A: Denote T as the total population of the country, denote S as the initial population in the country…

Q: The population of a district in a town is known to increase at a rate proportional to the number of…

A: We will find out the required initial population of the state .

Q: Let the height of an object bef(t)=t2+2t−4f(t)=t2+2t−4. What is the instantaneous rate of change of…

A: Given query is to find instantaneous rate of change of the object at t = 2.

Q: 10

A: We have, C(n) = (600+115n)/n = (600/n) + 115 So, C'(n) = - 600/n²

Q: Suppose that y is inversely proportional to the square of x, and that y=64 when x=5. What is y when…

A: Since  y is inversely proportional to the square of xy ∝1x2y =k 1x2where k is constant

Q: According to one simplified model, the purchasing power of a dollar in the year 2000 + t is equal to…

A:

Q: The number of children in a church is increasing at a rate that is proportional to the number of…

A: We will find the number of children after 5 years as following.

Q: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

A: given: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

Q: The population of Oregon was about 3,831,000 in 2010 and about 3,970,000 in 2014. Find the average…

A: The population of Oregon was about 3,831,000 in 2010 and about 3,970,000 in 2014.  The average rate…

Q: The Population of Barangay Siksikan is increasing at a rate proportional to its current population.…

A: ⁎ Given:        The population of Barangay Siksikan i.e, increasing     at a rate proportional to…

Q: A house sells for $81528 at the end of 2010 and for $161637 at the end of 2017.   If the market…

A:

Q: The rate at which yeast cells multiply is proportional to the number present. If the original number…

A: Given, The rate at which yeast cells multiply is proportional to the number present. the original…

Q: The median weight, ?, of a girl between ages 0 and 36 months can be approximated by the function ?…

A:

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We can find the answer as below.

Q: The population of the United States was 3.9 million in 1790 and 178 million In 1960. If the rate of…

A: Given,           The population of the United States was 3.9 million in 1790 and 178 million in…

Q: If a number decreases from 88 to 11, what is the rate of decrease (as a %)?

A: A number decreases from 88 to 11

Q: The gross domestic product (GDP) of a certain country was N(t) = t² + 5t + 106 billion dollars t…

A: Finding rate of change and percentage rate of change of GDP with respect to time using the given…

Q: C'(10) = 380,

A: Given: Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If…

Q: Find the Rate of Change of the gasoline usage. Gasoline Usage 15 14 13 12 11 10 25 50 75 100 125 150…

A: The given graph between Miles driven and Gasoline tanks usages. We have to find the rate of change…

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.