Question# 1

At the beginning of an experiment, a scientist has 204 grams of radioactive goo. After 180 minutes, her sample has decayed to 6.375 grams.

What is the half-life of the goo in minutes?__________

Find a formula forG(t), the amount of goo remaining at timett.G(t)=___________

How many grams of goo will remain after 11 minutes?_____________

Question# 2

The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 1 mg.

What was the initial mass (in mg) of the sample?___________

What is the mass 6 weeks after the start?___________

Question# 3

A bacteria culture initially contains 1500 bacteria and doubles every half hour.

Find the size of the baterial population after 60 minutes.__________

Find the size of the baterial population after 5 hours.___________

Question# 4

The doubling period of a bacterial population is10minutes. At time t=90minutes, the bacterial population was 80000.

What was the initial population at timet=0?____________

Find the size of the bacterial population after 4 hours____________

Question# 5

An object with an initial temperatureof 160Fis submerged in a large tank of water whose temperature is60F. Find a formula forF(t), the temperature of the object aftertminutes if the cooling constant isk=1.4

F(t)=______________

Question# 6

You go to the doctor and he gives you 14 milligrams of radioactive dye. After 16 minutes, 7.75 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.

Question# 7

The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 2000 years?

______________mg

Give your answer accurate to at least 2 decimal places

Question# 8

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 4 mg.

What was the initial mass (in mg) of the sample?__________________

What is the mass (in mg) 8 weeks after the start?_____________________

You may enter the exact value or round to 4 decimal places.

Question# 9

At the beginning of an experiment, a scientist has 400 grams of radioactive goo. After 240 minutes, her sample has decayed to 50 grams.

What is the half-life of the goo in minutes?_____________

Find a formula forG(t), the amount of goo remaining at timet. G(t)=_____________

How many grams of goo will remain after 53 minutes?______________

You may enter the exact value or round to 2 decimal places.

Question# 10

A bacteria culture initially contains 2500 bacteria and doubles every half hour.

Find the size of the baterial population after 40 minutes.______________

Find the size of the baterial population after 6 hours______________

Question# 11

The count in a bacteria culture was 400 after 20 minutes and 1900 after 35 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?___________

Find the doubling period.________________

Find the population after 65 minutes._____________

When will the population reach 15000._______________

You may enter the exact value or round to 2 decimal places.

Question# 12

The fox population in a certain region has a continuous growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 17000.

(a) Find a function that models the populationtyears after 2000 (t=0for 2000).

Hint: Use an exponential function with basee.

Your answer isP(t)=____________

(b) Use the function from part (a) to estimate the fox population in the year 2008.

Your answer is (the answer must be an integer)________________