You invest $1000 at an annual interest rate of r%, compounded continuously. At the end of 10 years, you have a balance of B dollars where B-g(r). What is the financial interpretation of g' (5) = 165? O (a) The balance in your account after 5 years is $165. O (b) The balance grows at a rate of $165 per % when r= 5%. O (c) If the interest rate increases from 5% to 6%, you would expect about $165 more in your account after 10 years. O (d) If the interest rate increases from 5% to 6% you would expect about $1814 in your account after 10 years.

Which of the following functions exhibits exponential decay? A (=) = (4)° fa (a) = 2" fa (2) = (-2)° fa (2) = 2-3

If $P is invested for n years at 12% compounded continuously, the future value that results after n years is given by the function S = Pe0.12n. (a) At what rate is the future value growing at any time (for any nonnegative n)? Your answer cannot be understood or graded. More Information = (u),s (b) At what rate is the future value growing after 1 year (n = 1)? S'(1) = %3D

The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 through 2019 can be approximated by the function P(x) = 166.61 e 0.03x, where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $208 million dollars? (b) If this model remains accurate, when would the total expenditures reach $482 million? (a) The expenditures would reach $208 million in the year mid- (Simplify your answer. Type a whole number.)