Your answer would be <u><em>27 Gallons.</em></u>
Staals half
1 gram left
0.3 grams left
half lives are normally written in years
it goes likt this
![A=P( \frac{1}{2})^ \frac{t}{h}](https://tex.z-dn.net/?f=A%3DP%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%5Cfrac%7Bt%7D%7Bh%7D%20%20)
A=final amount
P=initila amount
t=time elapsed
h=time half life is (same units as time)
let's use days as the units of time
we are given
initial amount=1gram
final amount=0.3gram
time=4 days
so
![0.3=1( \frac{1}{2})^ \frac{4}{h}](https://tex.z-dn.net/?f=0.3%3D1%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%5Cfrac%7B4%7D%7Bh%7D%20%20)
solve for h
![0.3=( \frac{1}{2})^ \frac{4}{h}](https://tex.z-dn.net/?f=0.3%3D%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%5Cfrac%7B4%7D%7Bh%7D%20%20)
take the ln of both sides
![ln(0.3)=ln( \frac{1}{2})^ \frac{4}{h}](https://tex.z-dn.net/?f=ln%280.3%29%3Dln%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%5Cfrac%7B4%7D%7Bh%7D%20%20)
![ln(0.3)=\frac{4}{h}ln( \frac{1}{2})](https://tex.z-dn.net/?f=ln%280.3%29%3D%5Cfrac%7B4%7D%7Bh%7Dln%28%20%5Cfrac%7B1%7D%7B2%7D%29%20%20%20)
times both sides by h
![hln(0.3)=4ln( \frac{1}{2})](https://tex.z-dn.net/?f=hln%280.3%29%3D4ln%28%20%5Cfrac%7B1%7D%7B2%7D%29%20%20%20)
divide both sides by ln(0.3)
![h= \frac{4ln( \frac{1}{2}) }{ln(0.3)}](https://tex.z-dn.net/?f=h%3D%20%5Cfrac%7B4ln%28%20%5Cfrac%7B1%7D%7B2%7D%29%20%7D%7Bln%280.3%29%7D%20)
use calculator
h=2.30287
3 sig figs
h=2.303 days
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It's 10 degrees I believe
Answer:
![y=13(4)^x](https://tex.z-dn.net/?f=y%3D13%284%29%5Ex)
Step-by-step explanation:
We have the exponential function of the form:
![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
And it goes through the points (0, 13) and (3, 832).
Hence, when we substitute in 0 for x, we should get 13 for y. Therefore:
![13=ab^0](https://tex.z-dn.net/?f=13%3Dab%5E0)
Since anything to the zeroth power is 1, this yields:
![a=13](https://tex.z-dn.net/?f=a%3D13)
So, we determined that the value of a is 13.
So, our function is now:
![y=13b^x](https://tex.z-dn.net/?f=y%3D13b%5Ex)
We will need to determine b. We know that y equals 832 when x is 3. Hence:
![832=13(b)^3](https://tex.z-dn.net/?f=832%3D13%28b%29%5E3)
Divide both sides by 13:
![b^3=64](https://tex.z-dn.net/?f=b%5E3%3D64)
Take the cube root of both sides:
![b=4](https://tex.z-dn.net/?f=b%3D4)
Hence, our b value is 4.
Therefore, our entire equation is:
![y=13(4)^x](https://tex.z-dn.net/?f=y%3D13%284%29%5Ex)