Exponential growth and decay practice problems
Exponential growth and decay: doubling time, half-life, and solving for the time. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
A bacteria culture starts with 100 cells and doubles every 4 hours. Find the number of cells after 7 hours, and how long it takes to reach 1000 cells.
A quantity grows exponentially: it is 200 at \( \displaystyle t = 0 \) and 300 at \( \displaystyle t = 3 \). Find it at \( \displaystyle t = 6 \), and when it reaches 2000.
A radioactive substance has a half-life of 30 years. Starting with 50 g, how much remains after 54 years, and when will only 10 g remain?
A quantity grows exponentially: it is 100 at \( \displaystyle t = 0 \) and 150 at \( \displaystyle t = 5 \). Find it at \( \displaystyle t = 10 \), and when it reaches 1000.
A bacteria culture starts with 1000 cells and doubles every 6 hours. Find the number of cells after 5 hours, and how long it takes to reach 5000 cells.
A bacteria culture starts with 1000 cells and doubles every 3 hours. Find the number of cells after 2 hours, and how long it takes to reach 10000 cells.
A radioactive substance has a half-life of 12 years. Starting with 250 g, how much remains after 23 years, and when will only 50 g remain?
A radioactive substance has a half-life of 1600 years. Starting with 250 g, how much remains after 2319 years, and when will only \frac{250}{3} g remain?
A quantity grows exponentially: it is 400 at \( \displaystyle t = 0 \) and 1000 at \( \displaystyle t = 5 \). Find it at \( \displaystyle t = 10 \), and when it reaches 4000.
A radioactive substance has a half-life of 30 years. Starting with 50 g, how much remains after 56 years, and when will only \frac{50}{3} g remain?