Problem 2.6 Suppose that the accumulation function for an account is a(t) = (1+0.5it). You invest $500 in this account today. Find i if the account's value 12 years from now is $1,250. Problem 2.8 Suppose a(t) = at2 + 10b. If $X invested at time 0 accumulates to $1,000 at time 10, and to $2,000 at time 20, find the original amount of the investment X. Problem 2.11 Suppose that you invest $4,000 at time 0 into an investment account with an accumulation function of a(t) = at2 +4ẞ. At time 4, your investment has accumulated to $5,000. Find the accumulated value of your investment at time 10.