54. Social Security beneficiaries Suppose the rate of change of the number of Social Security beneficiaries (in millions per year) can be modeled by dB 0.07149(0.1t + 1)? – 0.67114(0.1t + 1) + 2.2016 %3D dt where t is the number of years past 1950. Number Number of Beneficiaries of Beneficiaries Year (millions) Year (millions) 1950 2.9 2000 44.8 1960 14.3 2010 53.3 1970 25.2 2020 68.8 1980 35.1 2030 82.7 1990 39.5 Source: Social Security Administration

Q: The value of a car is decreasing by 1.5% per month. Suppose depreciation continues at this rate. (a)…

A: r=-1.5% suppose purchase price =p time ,when car price=p/2

Q: When a deposit of $1000 is made into an account paying 4% interest, compounded annually, the…

A: Given :   Formula for average rate of change :

Q: y = 10+7.5cos(0.507t). How quickly is the tide rising or falling (in meters/hour) at each of the…

A:

Q: Suppose that P dollars in principal is invested for t years at the given interest rates with…

A: Given that the Principal amount P=$16000Time t=11  years

Q: A=A0e^kt 2004 population (millions) Projected 2017 population (millions) Projected Growth rate K…

A: Given the data

Q: 5. The amount of pollution in the air is decreasing by 2.3% per week. (a) Approximately when will…

A: Let the current value of the pollution is= x     Given that the amount of pollution in the air is…

Q: Fund he lensm of he curce

A:

Q: find the accumulated amount after 3 years on an investment of 5000 earnings an interest rate of 5%…

A: given query is to find accumulated amount.

Q: Solve for "X" 10000* = 1/100000

A: 10000x=1100000104x=10-5

Q: If the marginal revenue (in dollars per unit) for a month is given by MR= -0.4x + 300, what is the…

A:

Q: The value, v of a computer is modeled by the function V(t)=500(0.82)^t where t is the number of…

A: The value of computer is modeled by the function,  V(t) = 500(0.82)t Where t is time in years

Q: Calculate the area A of the region between the two curves x = y +2y and x = y + 12. (Express your…

A:

Q: Data about the sound levels from a new speaker are collected at a manufacturing facility and are…

A: The objective of the question is to interpret the percent rate of change of the model in the context…

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.