Answer and Step-by-step explanation:
The answer is attached below
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
It is given in the question that
A projectile is fired at 657 mi/hr. how fast is that in meters per second? use the conversion factor 1 mile = 1610 m.
So we need to convert miles per hour to meters per second.
And it is given that 1 mile equals to 1610 meters and 1 hour equal to 3600 seconds.
So we will get
![657mi/hour = \frac{657*1610}{3600} m/seconds = 293.825m/s](https://tex.z-dn.net/?f=657mi%2Fhour%20%3D%20%5Cfrac%7B657%2A1610%7D%7B3600%7D%20m%2Fseconds%20%3D%20293.825m%2Fs)
Answer:
5x + 15
Step-by-step explanation:
To expand the binomial, you need to multiply each term inside the parentheses by 5.
(x + 3)5
= (x * 5) + (3 * 5)
= 5x + 15
Answer:
the second one for #4 and the third one for #5
Step-by-step explanation:
4. The sum of x and y is 24, so x+y = 24. The difference is 15, so x-y = 15, or
y-x=15 (they didn't specify which was which). Therefore, A, C, and D are correct, so x = 15-y is the answer (x = 15-y is the same as x+y = 15, which is false).
5.
Matt = 6 apple pies + 4 lemon pies and he got 80 dollars.
Ming = 6 apple pies + 5 lemon pies and he got 94 dollars.
If apple pie is "a" and lemon is "l":
6a + 4l = 80
6a + 5l = 94,
so C is the answer