Jennifer has several different kinds of investments, whose total value V(t) (in thousands of dollars) at the beginning of the tth year after she began investing is given in this table, for 1 ≤ t ≤ 10:

a. Modify the least-squares procedure, as illustrated in Example 7.4.4, to find a function of the form V(t) = Ae^rt whose graph best fits these data. Roughly at what annual rate, compounded continuously, is her account growing?

b. Use the function you found in part (a) to predict the total value of her investments at the beginning of the 20th year after she began investing.

c. Jennifer estimates she will need $300,000 to buy a vacation home. Use the function from part (a) to determine how long it will take her to attain this goal.

d. Jennifer’s friend, Frank Kornerkutter, looks over her investment analysis and snorts, “What a waste of time! You can find the A and r in your function V(t) = Ae^rt by just using V(1) = 57 and V(10) = 85 and a little algebra.” Find A and r using Frank’s method, and comment on the relative merits of the two approaches.

Transcribed Image Text:

Year t Value V(t) of all investments 1 2 3 57 60 62 4 45 65 5 S 66 62 65 7 8 9 10 70 75 79 85