Question

Solve the problem.

The profit made when t units are sold, t>, is given by P²-36t+320. Determine the number of units to be sold in order for P>0 (a profit is made).





The future value of $6000 invested for 5 years at rate r, compounded annually, is given by S=6000(1+r)^5. Find the rate r, as a percent that gives a future value of $8415.31. Round to the nearest whole percent.

Answer 1

S = 6000(1+r)^5 = $8415.31,
(1+r)^5 = 8415.31 / 6000 = 1.40255,
Take log of both sides:
5log(1+r) = log1.40255 = 0.1469,
log(1+r) = 0.1469 / 5 = 0.02938,
1+r = 10^0.02938
1+r = 1.06998,
r = 0.06998 = 6.998% = 7%.