(1) Radioactive Decay (use formulas given in class): Half-life of cesium-137 is 30 years. Assume we have a 10 gram sample.
(a) Determine function which models mass remaining after t years.
(b) How much of same will remain after eighty years?
(c) How long will it take same to reach mass of 2 grams?
(2) Population Growth (use exponential growth equation): Certain species of bird was introduced in certain country 25 years ago. Relative growth rate is 11% per year. It is evaluated that population recently was 18,000.
(a) Determine the function which models mass remaining after t years.
(b) What will bird population be in eight years?
(c) How long will it take population to reach about 90,000 birds?
(3) Compound Interest: Woman invests $65,000 in an account which pays 6.5% interest per year, compounded quarterly.
(a) How much will she have in account after five years?
(b) How long will it take for her account to reach $750,000?