The first thing we did dealt with was radioactive decay and half lives. The first question had to do with finding the amount of substance left after a determined amount of time; In our case, it was 3 years. So, all you have to do is substitute your X value for 3 and from there it becomes calculator work.
The next question involves a little more work and use of the logarithmic laws. We were asked to find the half life of the substance. What is asked here is what amount of time does it take for the substance to decay to half its original mass. So, we're solving for X. We know that the original mass was 80g so the mass at its half life would be 40g. Our Y value is now 40. Next, you multiply everything by ln. This is usually beneficial because out original question has the variable e in it so there is a good chance that we can get rid of it by using ln. Remember, the ln(80e^-0.2x) is actually ln80+ln(e)^-0.2x since it is a law. Next, we bring down the x value (another law) so we can factor it and get x by itself. From here, it becomes calculator work.
Out next section had to do with compound interest. Our first question had to do with finding the value of the investment after 1 year. All you have to do is substitute 1 in for the t value. From there it becomes calculator work.
The next question had to do with finding the value of the investment after 10 years. Again, just substitute 10 in for the t value and take it from there.
The last question had to do with finding the interest after 10 years. All you have to do for this is find the value of the investment after 10 years and subtract it from the original investment ($5000)
This formula shows what the interest would be if it was compounded all the time as opposed to just monthly or annually. How this formula was derived is that when the interest reaches a very high number, it gets very close to the value e. So the formula (1+r/n)^n simply becomes e^r. The reason why banks don't use this way of compounding interest is because it means more money for the consumer. The use of this formula is strait forward; You just substitute in your values and solve with your calculator.
The next section had to do with population increase. However, this formula can be used for anything that has to do with exponential growth. In this case, it ts used to show growth rates of bacteria. Also for this one, you just substitute in your values and solve.
Again, we are asked to find the half life of a substance. This question is just like the last one other than it is a different formula. You use natural logarithms to get rid of your e value, use the logarithmic laws, get x by itself, and solve with your calculator.
We were assigned 1-16 on exercise 26 and 1-10 on exercise 27.
I think we're assigned up to objective 31 on our accelerated math to be done before our test next Wednesday.
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