The bad news: Many of us have tiny cancer mini-tumors in us right now. Some theories suggest we may even be born with or even in the womb develop cancer cells.

Better news: But cheer up because, no one ever died of one or two or four cancer cells. It takes about a billion cells to be just about large enough to be detectable by, for example, a mammogram. What matters as clarified below, the rate at which the cancer cells divide.

Three Key Numbers:

1. Each "doubling" (from 1 cancer cell to 2, to 4, to 8, to 16 and so on) can take anywhere between 25 to 1,000 days.

2. One needs about 30 doublings to get to that small but significant, detectable tumor with about 1 billion cells

3. As one physician states that: it can therefore take between 2 and 100 years for a cancer cell to double and grow that large (1 billion cells) and he's not worried about it if it's growing so slowly that it will take about 100 years to become that lump - because he doesn't expect to live that lone (past 100) anyway. He'd be dying (from some other cause) just with (very small) cancer tumors in his body not dying from cancer.

The Really good news: Relatively new research findings suggest that adopting a healthier lifestyle (exercise and planet based nutrition) can have significant and even very rapid effects on that critical rate at which cancer cells divide and tumors grow.

More on that in a minute. First, a few related facts:

1. According to autopsy studies in Japan, they have just as much prostate cancer as we do in the U.S. but the rate of Japanese men dying from prostate cancer is just one-tenth (10%) of that of U.S. men. (unless/until they adopt SAD, the Standard American Diet....) This is despite the fact that Japanese men live long enough: Japan has the longest life expectancy of any nation (not counting sovereign "city-state" of Monaco) while the U.S. ranks far lower.

2. When Japanese men do eventually die, however, many have tiny prostate tumors. But the tutors were small enough that these men die "along with" their cancers, not from their cancer. They die from other causes before the cancer is large enough to hurt and kill them, in other words. Again the lesson: slowing the rate of growth can make a huge different

3. By age 80, the majority of men have tiny cancerous prostate tumors. And by age 40 one-third (33%) of women have microscopic cancerous breast tumors. Similarly many of us today have tiny cancerous tumors inside us but the key is: if we live by an enjoyable but healthy lifestyle that contributes to a slow growth rate, and slow doubling rate of the cancerous cells, we may live to a ripe old age and eventually, die "with our cancer" from some other causes in old age, but never die from our cancer.

4. See 4:10 minutes into this 5:49 min video here for the exciting findings of a UCLA research team of how exercise and a plant based diet changed the very blood composition of the participants in just two weeks so that growth rates of cancer cells (at least in vitro) with the blood dripped on them, were slowed significantly. That is, the cancer grew significantly more slowly when exposed to the blood of the women on the healthier diet-and-exercise regimen. If that can happen in just 2 weeks, imagine what a lifetime of healthier lifestyle might do to improve our odds. See dramatic images a bit after the 5:00minute mark, of how many fewer cancer cells "after" versus "before" lifestyle changes. Or watch the entire (just under) 6 minute video, well worth it for one's health. But first, on to the math, below!

1. First, confirm that claim that it takes "about 30 doublings" to get to 1 billion cancer cells. Try to do this in at least two ways

   Solution: Our calculator tells us that 2³⁰ = 1,073,741,824 or about 1 billion.

   Also, estimating without even needing a calculator,
   (Great for practice of estimation and of using several exponentiation properties) is possible:

   2³⁰ = (2¹⁰)³ = (1024)³ > (1,000)³ = (10³)³ = 10⁹ = 1 billion

2. Recall "Fact A" - that each "doubling" takes anywhere between 25 to 1,000 days. Now let's check the claim that this large variation in possible doubling times, means that the amount of time can range from "2 to 100 years" to reach that "1 billion cells" mark. Is this range of amount of time, in years, roughly in the right ballpark?

   Sample Solution/analysis:

   25 days/doubling · 30 doublings = 750 days = 750/365 years ≈ 2.05 years; just barely over 2 years (we ignore leap years here and below!)

   Versus if we have a healthy lifestyle consistently and other factors helping contribute to the slowest possible rate of doubling, we'd have:

   1,000 days/doubling · 30 doublings = 30,000 days ≈ 82.2 years.

   This is somewhat less than 100 years but not that far below; and remember, we're asking how long before we have a billion cells; the size where a lump can just begin to be detected by (for example) a mammogram, not the size that will kill you, let alone instantly kill you, which (if untreated and the worst happen) would take some extra time E years, for a total of 82+E years before fatality (even if the worst happened as far as treatment failing etc) about a human lifespan so you'd have a good chance of "dying with, but not dying from" the cancer. Especially if we add monitoring and sensible, carefully thought out treatment(s) if needed, on top of a life-long healthier lifestyle in terms of factors like diet and exercise. (video link)