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
Required Perimeter = AB + BC + CA
AB = sqrt((5 - (-1))^2 + (-1 - 1)^2) = sqrt(6^2 + (-2)^2) = sqrt(36 + 4) = sqrt(40) = 6.3
BC = sqrt((-1 - 0)^2 + (1 - (-3))^2) = sqrt((-1)^2 + 4^2) = sqrt(1 + 16) = sqrt(17) = 4.1
CA = sqrt((0 - 5)^2 + (-3 - (-1))^2) = sqrt((-5)^2 + (-2)^2) = sqrt(25 + 4) = sqrt(29) = 5.4
Perimeter = 6.3 + 4.1 + 5.4 = 15.8 units
Tony’s backpack can carry weight up to 22 but not more that that
If the variable n represents the total weight carried by tony
Then ; n less than or equal to (n=1+3+3b
=4+3b
Where b represents book
4+3b is less or equal to 22
3b is less or equal to 18
b is less or equal to 6
Therefore Tony’s backpack cannot carry more than 6 books