Decibel scale problems
You could even think of it like this: 10 4, 10 5, 10 6, and so on, which is commonly used and known as "scientific notation." That y-axis is a good example of a logarithmic scale. That's because it's not following a linear trend anymore every tick mark represents ten times the previous value. Notice how the y-axis of this plot looks all kinds of odd. This trend is known as "Moore's Law," named for the co-founder of computer supergiant Intel, Gordon Moore. The number of transistors on a single computer processor chip, which is a rough estimate of how powerful it is, doubles about every 18 months. The cool thing about computers is that as they get better, they help us make better computers, which yields better computers, which helps…well, you get the idea. This is thanks to the collective efforts of thousands of smart people all around the world.
Moore's LawĪ smartphone today is more powerful than the most powerful, room-filling supercomputers just a few decades ago. Sound intensity isn't quite the same thing as volume, though, but that's math for a rainy day. For every increase of the decibel level by 10, the sound intensity increases by 10 times the previous intensity. The decibel scale begins at 0, which is a "reference level" of sound intensity that humans can just barely hear. We can measure this intensity on the decibel scale, which is a logarithmic scale. Compared to a normal conversation, the sound at this concert is about 100,000 times more intense. What happens when you're at a loud rock concert? Your hair stands up, your brain hides in the corner of your skull, and your skin ripples in waves. That means f (0) = 20, so we can plug in 20 for f ( x) and 0 for x.Īt 4 seconds, x = 4, the bacteria doubles, so f (4)= 40. In the beginning of time, x = 0, there's 20 bacteria. What exponential function f ( x)= Cb x would model bacteria growth per second, assuming the bacteria split every 4 seconds and we start with 20 bacteria? In this case, we'll simplify any irrational numbers to four decimal places. If every bacterium splits into two, and those two bacteria split into two each, and so on, we've got an exponential function on our hands (Lucky us, right?) Sample Problem Those little buggers like to multiply like there's no tomorrow, through a process known as binary fission.
There are bacteria all around you: on the table, the bed, your pillow, inside of you. Let's start with something really yummy: bacteria. Most anything that starts slow and then increases really fast can be modeled using an exponential function, and similarly things that start quickly and then slow down in a hurry (oxymoron?) can often be modeled using a log function. Logs are everywhere, and so are exponents. Birch logs, mahogany logs, pine logs-okay, we'll stop there.