1. If 12900 dollars is invested at an interest rate of 6 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $
(b) Semiannual: $
(c) Monthly: $
(d) Daily: $
2. A radioactive substance decays at a continuous rate of
7
%
per day. After
7
days, what amount of the substance will be left if you started with
240
mg?
(a) First write the rate of decay in decimal form.
r
=
(b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.
3. The count in a bacteria culture was 400 after 15 minutes and 1000 after 30 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Find the doubling period.
Find the population after 110 minutes.
When will the population reach 13000.
You may enter the exact value or round to 2 decimal places.
4.The count in a bacteria culture was 400 after 15 minutes and 1000 after 30 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Find the doubling period.
Find the population after 110 minutes.
When will the population reach 13000.
You may enter the exact value or round to 2 decimal places.
5.You go to the doctor and he gives you 10 milligrams of radioactive dye. After 20 minutes, 7.5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm.
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived?
Give your answer to the nearest minute.
You will spend minutes at the doctor's office.
6.The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 6 mg.
What was the initial mass (in mg) of the sample?
What is the mass (in mg) 6 weeks after the start?
You may enter the exact value or round to 4 decimal places.
