Solved >     61.For the first week, the spread:1503885 …

 

 

61.For the first week, the spread of a rumor is proportional to the number of people who have heard the rumor.  Find the particular solution to the differential equation for N, the number of people who have heard the rumor as a function of time in days, t,  if 15 people have heard it at time t = 0, and 220 people have heard it at time t = 5.

A)      B)      C)      D) 

 

62.A country experiences a continuous inflation rate of about 5.5% per year.  If a t-shirt had a value of $14 in 1995, write a differential equation and use it to find what the t-shirt’s value was in 2005.  Round to the nearest cent.

 

63.If no more pollutants are dumped into a lake, the amount of pollution in the lake will decrease at a rate proportional to the amount of pollution present.  If there are 400 units of pollution present initially and 184 units left after 8 years, use differential equations to find the number of units left after 11 years.  Round to 1 decimal place.

 

64.On January 1, 1879, records show that 500 of a fish called Atlantic striped bass were introduced into the San Francisco Bay. In 1899, the first year fishing for bass was allowed, 100,000 of these bass were caught, representing 10% of the population at the start of 1899. Owing to reproduction, at any moment in time the bass population is growing at a rate proportional to the population at that moment.  Write a differential equation satisfied by B(t), the number of Atlantic striped bass a time t, where t is in years since January 1, 1879 and 0 ? t < 20 and solve it for B(t).

A)C)

B)D)

 

65.What is the general solution to the differential equation ?

A)      B)      C)      D)      E)  none of the above

 

66.You invest $6,500 in your nephew’s catering business.  He guarantees you a minimum return at a continuous interest rate of 3%.  Of course, if the business continues to thrive, you will earn at a higher rate.

 

a)  Write a differential equation for the minimum amount, B, of your return on investment at time t.

 

b)  Solve the differential equation.

 

c)  Graph the solution.

 

67.A certain bank account earns interest at the rate of 4% compounded continuously.  Money is being withdrawn from the account in a continuous stream at a constant rate of $100,000 per year.  Write a differential equation modeling how the balance B changes over time.  Which of the following is the general solution, given an initial balance of B0?

A)

B)

C)

D)

 

68.A certain bank account earns interest at the rate of 8% compounded continuously.  Money is being withdrawn from the account in a continuous stream at a constant rate of $100,000 per year.  Use differential equations to determine what the minimum initial balance should be in order for the account never to be depleted.

 

69.What is the general solution of  ?

 

70.What is the general solution of  ?

 

 

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