A small lake is stocked with a certain species of fish. The fish population is modeled by the function P = 14/1 + 4e-0.5t where P is the number of fish in thousands and t is measured in years since the lake was stocked.
(a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.)
(b) After how many years will the fish population reach 7000 fish? (Round your answer to two decimal places.)
A 15-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by m(t) = 15e-0.063t, where m(t) is measured in grams. After how many days is there only 3 g remaining? (Round your answer to the nearest whole number.)
Nancy wants to invest $2000 in saving certificates that bear an interest rate of 9.75% per year, compounded semiannually. How long a time period should she choose to save an amount of $4000? (Round your answer to two decimal places.)