HALF LIFE EXPONENTIAL WORD PROBLEMS WORKSHEET

Problem 1 :

The half-life of carbon-14 is known to be 5720 years. If 300 grams of carbon-14 are stored for 1200 years, how many grams will remain?

Solution

Problem 2 :

When Sophia drinks a brewed cup of coffee, she ingests 130 mg of caffeine into her system.

The half-life of caffeine in a typical adult is 5.5 hours. How much caffeine will be in her system 4 hours after she drinks the cup of coffee?

Solution

Problem 3 :

A colony of bacteria decays so that the population days from now is given by

n(t) = 1000(1/2)^t/4

a. What is the amount present when t = 0?

b. How much will be present in 4days?

c. What is the half-life?

Solution

Problem 4 :

The half-life of a radioactive isotope is 4 days. If 3.2 kg are present now, how much will be present after:

a. 4 days?

b. 8 days?

c. 20 days

d. t days?

Solution

Problem 5 :

The half life of radium is about 1600 years. If 1 kg is present now, how much will be present after 

a)  3200 years   b)  16000 years     c)  800 years

Solution

Problem 6 :

When a certain medicine enters the bloodstream, it gradually dilutes, decreasing exponentially with a half-life of 3 days. The initial amount of the medicine in the bloodstream is A₀ milliliters. What will the amount be 30 days later?

Solution

Problem 7 :

A culture starts with 1500 bacteria and the number doubles every 30 minutes.

In the half-life formula, use a 2 instead of 1/2 to find a function that models the number of bacteria at time t 

b. Find the number of bacteria after 2 hours.

c. After how many minutes will there be 4000 bacteria?.

Solution