Using exponential functions, it is found that:
a) Since the <u>amount of caffeine will be less than 50 mg</u>, the patient will be ready for the blood test by 6 a.m.
b) The patient could have ingest 231 milligrams of caffeine.
A decaying <em>exponential function</em> is modeled by:

In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem:
- Caffeine metabolize at a rate of 13% per hour, hence
.
Then:



Item a:
The coffee cup contains 150 milligrams of caffeine, hence
.
At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).



Since the <u>amount of caffeine will be less than 50 mg</u>, the patient will be ready for the blood test by 6 a.m.
Item b:
This A(0), considering <u>A(11) = 50</u>, hence:



The patient could have ingest 231 milligrams of caffeine.
A similar problem is given at brainly.com/question/25537936
Answer: First option.
Step-by-step explanation:
You can use the inverse tangent function to find the value of the angle T:

You can identify in the figure that:

Then, knowing these values, you can substitute them into
.
Therefore, you get that the value of the angle T rounded to the nearest degree is:

This matches with the first option.
Answer:
Purple line: 4
Red dashed line: 2
Blue line: 1/2
Step-by-step explanation:
The purple line is the steepest line, therefore it has the biggest constant of proportionality or slope. Since 4 is the biggest number among the others, we attribute it to the purple line (the one with the point C on it).
Think of it this way:

here
so 
The greater a is, the greater y is. So for any value of x, y will be become bigger and bigger if we increase the value of a.
Take for example this one:

Take
therefore
Now take
and take
therefore
When we increased this constant of proportionality, as you can see from 2 to 4, the value of y increase from 4 to 8.
Hope this is helpful. Think of it really carefully, and I'm sure you'll grasp the concept.
D is most likely the answer.
Hope this Helped!
;D
Brainliest??
Because we have to evaluate was in the parenthesis and then solve it, then we need to remember to multiply first before going to the addition