Because of the popularity and power of smartphones, demand for wireless communication is growing rapidly. Suppose monthly global data traffic is predicted to be 4.5e0.573x petabytes, where x is the number of years since 2015. Find the relative growth rate in any year x.

Q: suppose the population of a certain bacteria in a laboratory sample is 100. if it is doubles in…

A: Given: The population of a certain bacteria in a laboratory sample is 100 and it is doubles in…

Q: If a population is recorded at 1,200 in the year 2000 and the rate of increase is a steady 50 people…

A: Given date  Initial population Po=1200 in the year 2000 (t=0) Rate of increase is a steady =50…

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

A: Given the development of the iPod that includes the stock price of Apple in which it grows rapidly…

Q: The growth rate G of a population of animals in a conservancy was documented. If the growth rate…

A:

Q: A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a)…

A:

Q: The population of a certain city was 34000 in 2010, and the observed relative growth rate is 0.5%…

A: Given information : Population of city in 2010 = 34000 Relative growth rate = 0.5%

Q: if the population of Palestine is 6 million in 2020  with a growth rate of 3%/yr when it is expected…

A: Given: The population of Palestine is 6 million in 2020  with a growth rate of 3%/yr

Q: The Loth Cat population grows at a constant relative growth rate. If the population is 400 after 2…

A: Let the constant relative growth rate be 'r' and the time in years be 't'. Let the population at any…

Q: sketch the shifted exponential curves

A: We have to sketch the shifted exponential curves: y=-ex and y=-e-x. We know the graph of ex and e-x,…

Q: Can the average rate of change of an increasing function ever be negative?

A:

Q: Estimate the average rate of change for the graph above from x=1x=1 to x=4

A:

Q: Five years ago a family was in debt $9.000. They are now in debt $10,000. Assuming their…

A: Given that indebtedness of the family is changing at a rate proportional to their indebtedness. Five…

Q: Explain the method of fitting of an exponential curves of the form (i)Y = abX and (ii) Y = aebx to…

A:

Q: Find the equation of the graph and estimate the instantaneous rate of change at x = 1

A: From graph we can conclude that the equation of this graph be a parabola i.e., a quadratic equation.…

Q: A certain stock has grown continuously from 1980 to 2015. A $15,000 investment in the stock in 1980…

A: A certain stock has grown continuously from 1980 to 2015. A $15,000 investment in the stock in…

Q: The average levels of particulate matter (PM2.5), a key cause of adverse health effects associated…

A: By using linear relation in level of PM2.5 and Year, we can find the PM2.5 level in year 2022

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

Q: Find the present value of $2000 to be received in 10 years, if money may be invested at 8% with…

A:

Q: Consider a population that begins growing exponentially at a base rate of 8​% per year and then…

A:

Q: If there are 520 grams of Tadioactive material with a half-life of 12 hours, how TIuch of the…

A: The material is decaying at a constant rate, every 12 hours it is getting halved.  So, it is an…

Q: If the starting point is 900, and the decay rate is 3%, choose the exponential function.

A: Starting point refers to the initial value. Decay rate is 3% = 0.03

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: What happens to the rate of change of the exponential function y = ax as a becomes larger?

A: To explain the given problem

Q: If a piece of machinery depreciates continuously at an annual rate of 4%, how many years will it…

A: To find: The number of years it will take for the value of machinery to halve. Concept used: The…

Q: If population y grows at a rate proportional to the current population, then y could be

A: This make separable differential equation

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 a population that begins growing exponentially at a base rate of 4.1​% per year and then…

A: Given that a population is begins growing exponentially at a base rate of  r=4.1% per year and then…

Q: Suppose that a business provides a continuous income stream with an annual rate of flow at time t…

A:

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: We have to find the growth rate.

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: An Asian country had a population of about 0.90 Billion people in 1995 and a growth rate of 1.3% per…

A: *** This is the problem related to financial mathematics and we are advanced math expert and have…

Q: Suppose the amount of oil pumped from one of the canyon wells in Whittier, California, decreases at…

A: To determine the time (in years), the output of well fall to 1/5 of its present value.

Q: An environmental study of a certain community suggests that t years from now the level of carbon…

A: Let's find.

Q: What value of the smoothing constant would make an exponential smoothing forecast the most reactive…

A: We know the smoothing exponential formula Ft+1=Ft+αDt-Ft where, α=smoothing constant Ft+1=forecast…

Q: model a population p if its rate of growth is proportional to the amount present at time t

A: model a population p if its rate of growth is proportional to the amount present at time t

Q: The population of Mathlandia in 1995 was 23,473 and was projected to grow at a rate of 12% per…

A:

Q: The manufacturer's suggested retail price (MSRP) for a particular car is $24,805, and it is expected…

A:

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

A:

Q: A network server has an original value of 10, 000 and is to be depreciated linearly over 5 years…

A:

Q: If a new car is valued at $20,600 and 8 years later it is valued at $3000​, then what is the average…

A: Given that the value of a new car is $20,600 and 8 years later it is valued $3,000.The initial value…

Q: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

A:

Q: Suppose you invest $2000 at a rate of 3.25% continuously, what is the worth of the investment after…

A: Given that P = $2000  rate of Interest = 3.25% continuously, we have to find what is the worth of…

Q: If g(x) = 3x3 + 6x2 + 4. What is the value ofthe instantaneous rate of change of g(x) when x = -1?

A: We have to solve the problem

Q: Suppose that a population in a particular city is 46,581 in 2010. What is the population after 15…

A: The population growth is modelled using the equation: N(t)=N01+rt, where N0 is the initial…

Q: Suppose a variable is growing continuously at a nominal rate of 10% per year. What is the effective…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A:

Q: If we have a formula giving the cholesterol level of a patient as a functionof time, how can we find…

A: Integration gives the function whose derivative is given. Integration means adding all slices to…

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: a 2012 article in the Los Angeles times reported that the number of weekly visits to Pinterests web…

A: The number of visitors in the year 2011 = 1.27 million Percentage increase = 2183% every year So the…

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.