Answer:
240+30x
Step-by-step explanation:
240+30x because you multiply 30 x 8 and get 240 plus 30 x X and get 30x
Answer:
Step-by-step explanation:
Please view the attached file.
To answer this question, we can set up a proportion:
![\frac{40g}{12oz} =\frac{25g}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B40g%7D%7B12oz%7D%20%3D%5Cfrac%7B25g%7D%7Bx%7D%20%20)
Then we cross multiply and solve for x:
![40x=300](https://tex.z-dn.net/?f=%2040x%3D300%20)
![x=7.5oz](https://tex.z-dn.net/?f=%20x%3D7.5oz%20)
So you can drink 7.5 oz of the Dr. Pepper in one day.
Answer:
![\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D4%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Ex)
Step-by-step explanation:
<u>Exponential Function</u>
The exponential function can be written with the general equation:
![f(x)=A\cdot r^x](https://tex.z-dn.net/?f=f%28x%29%3DA%5Ccdot%20r%5Ex)
Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.
The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.
Substituting in the third function:
![\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D4%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Ex)
![\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%280%29%3D4%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E0)
![f(0) = 4](https://tex.z-dn.net/?f=f%280%29%20%3D%204)
This gives the correct value of f(0)=4.
Substituting in the fourth function:
![\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Ex)
![\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%280%29%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E0)
![f(0) = \frac{1}{2}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
This choice is wrong
Correct choice:
![\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20f%28x%29%3D4%5Ccdot%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Ex%7D)