I need help on my 3rd recent question asap.

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.

After hearing a knock at your front door, you are surprised to see the prize patrol from a large, well-known magazine subscription company. it has arrived with the good news that you are the big winner, having won $21 million. you have three options.(a) receive $1.05 million per year for the next 20 years.(b) have $8.25 million today.(c) have $2.25 million today and receive $750,000 for each of the next 20 years.your financial adviser tells you that it is reasonable to expect to earn 13 percent on investments.

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?