For Wyatt's recipe the rate is:
r1 = 3.15 / 9
r1 = 0.35
For Cora's recipe the rate is:
r2 = 2.4 / 8
r2 = 0.3
The difference between both recipes is:
r1-r2 = 0.35 - 0.3 = 0.05
Answer:
0.05 cups of flour per shortcake less is needed for Cora's recipe
what else? ................
Answer:
820
Step-by-step explanation:
100j+40h
100(5)+40(8)
500+320
820!
Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:
![A(t) = A(0)e^{-kt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-kt%7D)
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus,
. We use this to find k.
![A(t) = A(0)e^{-kt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-kt%7D)
![0.7278A(0) = A(0)e^{-10k}](https://tex.z-dn.net/?f=0.7278A%280%29%20%3D%20A%280%29e%5E%7B-10k%7D)
![e^{-10k} = 0.7278](https://tex.z-dn.net/?f=e%5E%7B-10k%7D%20%3D%200.7278)
![\ln{e^{-10k}} = \ln{0.7278}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-10k%7D%7D%20%3D%20%5Cln%7B0.7278%7D)
![-10k = \ln{0.7278}](https://tex.z-dn.net/?f=-10k%20%3D%20%5Cln%7B0.7278%7D)
![k = -\frac{\ln{0.7278}}{10}](https://tex.z-dn.net/?f=k%20%3D%20-%5Cfrac%7B%5Cln%7B0.7278%7D%7D%7B10%7D)
![k = 0.03177289938 ](https://tex.z-dn.net/?f=k%20%3D%200.03177289938%0A)
Then
![A(t) = A(0)e^{-0.03177289938t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.03177289938t%7D)
What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So
![A(5) = A(0)e^{-0.03177289938*5}](https://tex.z-dn.net/?f=A%285%29%20%3D%20A%280%29e%5E%7B-0.03177289938%2A5%7D)
![A(5) = 0.8531](https://tex.z-dn.net/?f=A%285%29%20%3D%200.8531)
The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.