Answer:
Step-by-step explanation:
<h3>Given</h3>
- P = $720
- F = $735
- r = 1.74%
- Compound n = 4t
- Time = t = ?
<h3>Solution</h3>
- 735= 720*(1 + 0.0174/4)^n
- 1.00435^n = 735/720
- 1.00435^n = 1.02083333333
- log 1.00435^n = log 1.02083333333
- n= log 1.02083333333 / log 1.00435
- n = 4.75
- t = 4.75/4
- t = 1.1875 = 1.19 rounded to 2 decimal places
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.
Answer:
x = 6
Step-by-step explanation:
The ratio of consecutive terms is the same, so we have ...
x/3 = (x +6)/x
x^2 = 3(x +6) . . . . . . multiply by 3x
x^2 -3x -18 = 0 . . . . subtract 3(x+6), simplify
(x -6)(x +3) = 0 . . . . factor
x = 6 . . . . . . . . . the only possible positive value
___
<em>Additional comment</em>
The zero product rule tells you that a product will be zero if and only if a factor is zero. That is, the solutions to this equation are values of x that make the factors zero: x = 6, x = -3.
Answer:
Check explanation below!
Step-by-step explanation:
» <u>Solving</u>
Step 1: Subtract 4x from both sides.
Step 2: Divide both sides by -5.
First step is to convert gallons to liters. The equation would be 1.5(3.785) = x.
Solve for x, so that you convert 1.5 gallons to liters, equaling 5.6775 liters. Then, you convert liters to milliliters. 5.6775 liters = 5677.5 milliliters.
The answer is the third answer, 5677.5 ml.