Answer:
how much was originally?
Step-by-step explanation:
Answer: I need the table to give the answer
Step-by-step explanation: copy and paste the table
Using an exponential function, it is found that:
a) ![N(t) = 75(0.5)^{\frac{t}{3.8}}](https://tex.z-dn.net/?f=N%28t%29%20%3D%2075%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D)
b) 37.5 grams of the gas remains after 3.8 days.
c) The amount remaining will be of 10 grams after approximately 11 days.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
Item a:
We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:
![N(t) = 75(0.5)^{\frac{t}{3.8}}](https://tex.z-dn.net/?f=N%28t%29%20%3D%2075%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D)
Item b:
This is N when t = 3.8, hence:
![N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5](https://tex.z-dn.net/?f=N%28t%29%20%3D%2075%280.5%29%5E%7B%5Cfrac%7B3.8%7D%7B3.8%7D%7D%20%3D%2037.5)
37.5 grams of the gas remains after 3.8 days.
Item c:
This is t for which N(t) = 10, hence:
![N(t) = 75(0.5)^{\frac{t}{3.8}}](https://tex.z-dn.net/?f=N%28t%29%20%3D%2075%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D)
![10 = 75(0.5)^{\frac{t}{3.8}}](https://tex.z-dn.net/?f=10%20%3D%2075%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D)
![(0.5)^{\frac{t}{3.8}} = \frac{10}{75}](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D%20%3D%20%5Cfrac%7B10%7D%7B75%7D)
![\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}](https://tex.z-dn.net/?f=%5Clog%7B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B3.8%7D%7D%7D%20%3D%20%5Clog%7B%5Cfrac%7B10%7D%7B75%7D%7D)
![\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B3.8%7D%5Clog%7B0.5%7D%20%3D%20%5Clog%7B%5Cfrac%7B10%7D%7B75%7D%7D)
![t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}](https://tex.z-dn.net/?f=t%20%3D%203.8%5Cfrac%7B%5Clog%7B%5Cfrac%7B10%7D%7B75%7D%7D%7D%7B%5Clog%7B0.5%7D%7D)
![t \approx 11](https://tex.z-dn.net/?f=t%20%5Capprox%2011)
The amount remaining will be of 10 grams after approximately 11 days.
More can be learned about exponential functions at brainly.com/question/25537936
Answer:
-2/3 is the y intercept
Step-by-step explanation:
So to find the y-intercept you must first put this in Slope-intercept form, I believe the form it is in right now is called standard form.
To get it into slope intercept form, we have to isolate y:
subtract 2x from both sides:
-3y = -2x + 2
Divide both sides by -3:
y = (2/3)x - 2/3
Now that we have slope-intercept form, we can find the y-intercept. We know slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case the y-intercept is -2/3.
Hope this helps!
Answer:
31.5214 cm
Step-by-step explanation: