Answer:
amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
Step-by-step explanation:
Given: The function
represents number of milligrams of a drug in a person’s body after t hours
To find: time after which amount of the drug becomes approximately 0.2 milligrams
Solution:
![f(t)=10e^{-0.3 t}\\0.2=10e^{-0.3 t}\\\frac{0.2}{10}=e^{-0.3 t}\\\frac{2}{100}=e^{-0.3 t}\\\frac{1}{50}=e^{-0.3 t}\\](https://tex.z-dn.net/?f=f%28t%29%3D10e%5E%7B-0.3%20t%7D%5C%5C0.2%3D10e%5E%7B-0.3%20t%7D%5C%5C%5Cfrac%7B0.2%7D%7B10%7D%3De%5E%7B-0.3%20t%7D%5C%5C%5Cfrac%7B2%7D%7B100%7D%3De%5E%7B-0.3%20t%7D%5C%5C%5Cfrac%7B1%7D%7B50%7D%3De%5E%7B-0.3%20t%7D%5C%5C)
As
,
![50=e^{0.3 t}\\0.3t=\ln 50\\t=\frac{\ln 50}{0.3}=13.04\,\,hours](https://tex.z-dn.net/?f=50%3De%5E%7B0.3%20t%7D%5C%5C0.3t%3D%5Cln%2050%5C%5Ct%3D%5Cfrac%7B%5Cln%2050%7D%7B0.3%7D%3D13.04%5C%2C%5C%2Chours)
So, amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
Answer:
no solution
Step-by-step explanation:
when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.
Answer: It would take Tanya 15 minutes to run 2 kilometers
Answer: 15 minutes
Step-by-step explanation: This is true because:
If Tanya can run 8 kilometers in an hour (60 minutes) and you need to find how long it takes for her to run 2 kilometers there are two ways you can solve this:
#1: You find the unit rate (how long it takes Tanya to run 1 kilometer).
This would be written as 8 kilometers divided by 60 minutes. Once you do that math, you should get 7 1/2 minutes for one kilometer. However, since she is running 2 kilometers, you would multiply 7 1/2 by 2 to get your answer, which is 15 minutes.
#2: You set up a proportion to solve this problem:
This would be written as:
8/60 == 2/x, where the numerator of each fraction is the number of kilometers ran, the denominator is how long it took to run that distance, and x is the amount of minutes it took Tanya to run 2 kilometers. If you cross multiplied, you would get the following equation:
8x=120.
To get x by itself, you would divide both sides by 8; 8x/8 is x, and 120/8 is 15, getting you an answer of x=15, or 15 minutes.
Answer:
The equation of the line that passes through the point (-2,0) with a slope of -1/3 is y= -1/3x-2/3