Ending Amount = Beginning Amount * e^k*t
5 grams = 100 grams * e^-.00043 * years
We have to solve the equation for "years"
(You can find the formula here: http://www.1728.org/halflif2.htm
or you can just read the next line
time = natural log (bgng amt / endg amt) / k
time = natural log (100 / 5) / .00043
time = natural log (20) / .00043
time = 2.9957322736 / .00043
time =
<span>
<span>
<span>
6,967</span></span></span><span> years
</span>
We should double-check this.
First, we need the half-life
k = ln(.5) / half-life
half-life = <span>-.693147 / -.00043
half-life = 1,612 years
Now let's see how many half-lives that is:
</span><span>6,967 / 1,612 years = 4.2 half-lives
So basically, after 4 half-lives the mass should go from
100
50 1 half life
25</span><span><span> 2 half lives</span>
12.5 </span><span>3 half lives
</span> 6.25 <span>4 half lives</span>
6.25 is very close to 5 grams so we can assume we have calculated correctly.
Here's a couple of ideas.
1) Use concept of rational numbers.
Start by assigning 2 variables with a square root, representing each student.
Then multiply the 2 variables together resulting in a whole number. (canceling the square root)
Then say that being by yourself is irrational. But working together is rational.
2) Set up a linear equation to show how the more they work together the higher their grades will be.
For 8th grade a simple one is all that is needed.
where t is hours working together.
Provide a graph or table demonstrating the positive slope.
Good luck
Answer:
Step-by-step explanation:
For sales tax, you just have to multiply the percentage by the number. So you can only have one step, add 1 after you divide the percentage by 100.
45.5•1.07=48.685
The cent only goes to the hundredths, so we have to round.
The total amount is $48.69.
Perimeter = 9 + 13 + 6 = 28 m
area = 1/2 x 9 x 5.3 = 23.85 square m