The number of daily users for Japan’s Line messaging service (in millions) can be approximated by the function g(x)=53.1+63.1ln(x) corresponds to the first quarter of 2013. Numbering quarters from that date, and assuming the model remains accurate, find the first full quarter in which the number of users exceeded 200 million.

Q: of tax returns that will be electronically filed for 2010 using exponential smoothing with α=0.1

A: Solution

Q: The amount of plutonium remaining from 1 kilogram after x years is given by the function…

A:

Q: The number of insects in a colony is known to multiply at a rate proportional to the number of…

A:

Q: A newspaper headline states that “The rate of growth of the national deficit is decreasing.” What…

A:

Q: Over the past fifty years the carbon dioxide level in the atmosphere has increased. Carbon dioxide…

A:

Q: Explain a general mathematical modeling to growth of Human population. And what will be the Iraq…

A: Let the population of Iraq at time t is:  y(t) Therefore: dydtα y

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

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: Find the instantaneous rate of change of the function at the given value f(x)=6x2-4x+3; x=2

A:

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

A: This question is related to the population growth, We will solve it using integration.

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells.Write…

A:

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

A:

Q: The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an…

A: bn=2.520n & rn=441,000n a). an=bn-rn=2.520n-441,000n=-4,40,997.48n

Q: Since January 1980, the population of the city of Brownville has grown according to the mathematical…

A:

Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had…

A: Given,           In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the…

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

A: Given: C=0.2x2+10,000

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

A: Initial population =45000 Growth Rate=3%=0.03 At 2016, t=2016-2015=1 So the population in 2016 is:

Q: Suppose an unknown radioactive substance produces 22400 counts per minute on a Geiger counter at a…

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about…

A: Given: y=y0e-0.0001216t

Q: A factory machine was purchased for $45,000 and has an estimated lifetime of 8 years. If the scrap…

A: Solution:   Initial Value = 45000 Final Value =  3000 rate of depreciation = r t = Time period = 8…

Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

A: The general growth formula is given by,

Q: If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink. Iodine 131…

A: Given:- If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink.…

Q: According to the Social Security Advisory Board, the number of workers per beneficiary of the Social…

A: Calculation:a)From the given, it is observed that the initial value is 3.3 and the constant…

Q: Estimate the value of x to the nearest tenth when the y-value of the exponential function begins to…

A:

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: write down the solution parameters of this graph. what is the: -scale factor -starting x value…

A: Given graph: There is no Linear 2 and Exponential 2 graph. To find: Scale factor Starting x-value…

Q: The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function…

A:

Q: The population of Tagum City is increasing at the rate proportional to its current population. In…

A:

Q: Estimate the value of x to the nearest tenth when the y-value of the exponential function begins to…

A: We have to estimate the value of x to the nearest tenth when the y-value of the exponential function…

Q: city of half a million, there are initially 400 cases of a particularly virulent strain of flu. The…

A:

Q: The number of bacteria in a liquid culture is observed to grow at a rate proportional to the number…

A: We know that at the beginning of the experiment, number of cells = 104 After 3 hours of the…

Q: Find a formula for the derivative of the function 2x2 – 3

A:

Q: The equation y=5x+3 represents an exponential function. How are the y-values related for points…

A:

Q: Find the instantaneous rate of change for the function: f (x)= 4x = 2x²- 5

A: The instantaneous rate of change of function will be find by differentiate the function with respect…

Q: If in the year 2000 there were 1.26 million metric tons of beef produced and demand is growing at a…

A:

Q: A slightly different breed of Hippogriffs, living in the Rathlin Island—the northernmost point in…

A:

Q: An initial investment of $6000 grows at 5% per year. What function represents the value of the…

A: Given that initial investment made = $6000 It is said that the investment grows 5% per year. This is…

Q: The equationx - y2 = 0 implicitly defines whattwo functions?

A: x-y2=0 Now solve for y  y2=xy=±x  , x>0

Q: Statistics complied by the local department of corrections indicate that x years from now the number…

A:

Q: . Write the equation of a function if its rate of changeis -15 and its initial value is 12.

A: Given:- Initial value of a function = −15 Rate of change of function = 12 To find equation.

Q: What are the linear and exponential functions whose graphs contain the points (0,4) and (3,108)?

A: Here we have to find the linear and exponential functions whose graphs contain the points (0,4) and…

Q: There were around 70,000 black rhinos in the world in 1970. After that, their population declined by…

A:

Q: On the basis of data for the years 1911 through 1994, the expected life span of people in a country…

A: f(x) = 12.469 lnx +17.128x is the number of years from 1906 to person's birth year.expexted life…

Q: The population of an endangered species decreases at a rate of 7% per year. Approximately how long…

A: Answer

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: A scientist discovered a new material that expands at an extremely fast rate. After studying…

A: We have to use exponential growth function to solve the problem

Q: The price of a computer component is decreasing at a rate of 13​% per year. State whether this…

A: The price of a computer component is decreasing at 13% per year. Now, let the initial price of the…

Q: Calculate the instantaneous rate of change for the function f(x)=2/3x+5 when x=-7

A: The function is f(x) = 2/(3x + 5). We have to calculate the instantaneous rate of change for this…

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

A:

Q: at what point on the graph of f(x)= (x-8)(x-2)/x-4 would you not be able to determine the…

A: Given:   To find: The point at which instantaneous rate of change cannot be determined.

Q: A company selling widgets has found that the number of items sold z depends upon the price p at…

A: A company selling widgets has found that the number of items sold x depends upon the price p at…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.