Bob and Laura Mackenzie have a new grandchild, Brenda. They want to create a trust fund for her that will yield $200,000 on her 25th birthday. a) What lump sum would they have to deposit now at 5.2%, compounded continuously, to achieve $200,000? b) Bob and Laura decide instead to invest a constant money stream of R(t) dollars per year. Find R(t) such that the accumulated future value of the continuous money stream is $200,000, assuming an interest rate of 5.2%, compounded continuously. . .. a) To achieve $200,000, they would have to deposit $ (Round to the nearest cent as needed.) In 2002 (t = 0), the world consumption of a natural resource was approximately 18 trillion cubic feet and was growing exponentially at about 5% per year. If the demand continues to grow at this rate, how many cubic feet of this natural resource will the world use from 2002 to 2004? . . . The approximate amount of resource used is trillion cubic feet. (Round up to the nearest trillion.) A radioactive chemical has a decay rate of approximately 10% per year. Suppose that this chemical is released into the atmosphere each year for 18 yr at a constant rate of 3 lb per year. How much of this chemical will remain in the atmosphere after 18 yr? The amount of chemical remaining in the atmosphere is lbs. (Type an integer or decimal rounded to the nearest hundredth as needed.)