Anything that grows at a rate proportional to its own size doubles in a fixed time, whatever it started at. That one fact is what half-life and doubling time both mean.
A culture doubles every 3 hours. It starts at 80 bacteria. How many after 12 hours?
Twelve hours is four doubling periods.
So the count is 80 times 2 to the fourth.
That is 1280.
The answer is 1280.
Where students go wrong
Multiplying by the number of periods instead of raising to it. Four doublings is not four times as many, it is sixteen times as many, because each doubling acts on what the last one left.
Also called half life, doubling time, continuous growth, radioactive decay, exponential growth and decay or population growth.
Questions about these worksheets
Yes. Every half-life and doubling time sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the half-life and doubling time questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Multiplying by the number of periods instead of raising to it. Four doublings is not four times as many, it is sixteen times as many, because each doubling acts on what the last one left.