The automobile assembly plant you manage has a Cobb-Douglas production function given by P = 30x^0.6y^0.4 where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget(in dollars). You maintain a production level of 800 automobiles per year. If you currently employ 120 workers and are hiring new workers at a rate of 20 per year, how fast is your daily operating budget changing?

Q: Suppose that the population in a small city is 36000 in the beginning of 2007and the city council…

A: The model for the population of the city is given as     P = 36000e0.03t  We need to determine the…

Q: Suppose the income from an Internet access business is a continuous income stream with annual rate…

A: We have given the rate of annual flow,f(t)=900 t e-0.1t

Q: Median household income sharply increased in 2015 by 5.2% but only grew by 1.8% in 2017 to $61,372.…

A: a) Assume the median income in 2016 is x.

Q: Tuberculosis (TB) is one of the top 10 causes of death worldwide. According to the World Health…

A:

Q: A water tank has been sanitized by pouring in chlorine bleach. Bleach is toxic at the level needed…

A:

Q: Suppose a county's population can be approximated with the function P(t)=34(1.00804)^t where t is…

A: Given t  is the number of years since 2000 So, 2000 means t=0  At t=0  So the population of 2000 is…

Q: ↑ Using actual and projected data from 2000 through 2050, the number of millions of white…

A:

Q: Personal care aid is an occupation that is growing quickly. Assume that, in a certain region there…

A: Given information:The number of personal care aids in 2024 is 157,500, which is a growth of 28% over…

Q: opulation growth models are given for countries based on the World Health Organization’s 2006 World.…

A: Given that: R(t)=9.038(1.05)t H(t)=10.098(0.998)t     NOTE: As per our answering guidelines, we can…

Q: A cyclist is tracking weekly mileage while training for a race. The table models the number of…

A: x(weeks)01234y (miles)607286.4103.68124.416

Q: The population of the world in 1987 was 5 billion and the growth rate was estimated at 7 percent per…

A: we need to find the projected world population in 1999 =Population1987*(1+7%)^(1999−1987)

Q: Explain how the growth rate function can be decreasing while thepopulation function is increasing.

A: Explain the reason behind that the growth rate function can be decreasing while the population…

Q: In mid to late March a COVID analyst predict the number of US cases could be modeled by the function…

A: Given: In mid late March a COVID analyst predict the number of US cases could be modeled by the…

Q: Suppose that the online retailer Amazon needs to use larger and larger cardboard boxes over time.…

A: It is given that, the volume increases by 80 cubic inches each year and  height increases by 0.5…

Q: average cost per gigabyte of RAM can be approximated by the function C(t)= 8,500,000(0.65)^ t, where…

A: Given query is to find the the average cost of ram for the given time.

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.