Using an exponential function, it is found that there will be only 3 milligrams remaining in the patient's system after 201 minutes.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, initially, there are 11 milligrams on the patient's system, hence A(0) = 11. After 70 minutes there are 7 milligrams, hence A(70) = 7, and this is used to find r.
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
![7 = 11(1 - r)^{70}](https://tex.z-dn.net/?f=7%20%3D%2011%281%20-%20r%29%5E%7B70%7D)
![(1 - r)^{70} = \frac{7}{11}](https://tex.z-dn.net/?f=%281%20-%20r%29%5E%7B70%7D%20%3D%20%5Cfrac%7B7%7D%7B11%7D)
![\sqrt[70]{(1 - r)^{70}} = \sqrt[70]{\frac{7}{11}}](https://tex.z-dn.net/?f=%5Csqrt%5B70%5D%7B%281%20-%20r%29%5E%7B70%7D%7D%20%3D%20%5Csqrt%5B70%5D%7B%5Cfrac%7B7%7D%7B11%7D%7D)
![1 - r = \left(\frac{7}{11}\right)^\frac{1}{70}](https://tex.z-dn.net/?f=1%20-%20r%20%3D%20%5Cleft%28%5Cfrac%7B7%7D%7B11%7D%5Cright%29%5E%5Cfrac%7B1%7D%7B70%7D)
1 - r = 0.99356387084
r = 1 - 0.99356387084
r = 0.00643612916
Hence the equation for the amount after t minutes is:
![A(t) = 11(0.99356387084)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%2011%280.99356387084%29%5Et)
In will be of 3 mg when A(t) = 3, hence:
![A(t) = 11(0.99356387084)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%2011%280.99356387084%29%5Et)
![3 = 11(0.99356387084)^t](https://tex.z-dn.net/?f=3%20%3D%2011%280.99356387084%29%5Et)
![(0.99356387084)^t = \frac{3}{11}](https://tex.z-dn.net/?f=%280.99356387084%29%5Et%20%3D%20%5Cfrac%7B3%7D%7B11%7D)
![\log{(0.99356387084)^t} = \log{\left(\frac{3}{11}\right)}](https://tex.z-dn.net/?f=%5Clog%7B%280.99356387084%29%5Et%7D%20%3D%20%5Clog%7B%5Cleft%28%5Cfrac%7B3%7D%7B11%7D%5Cright%29%7D)
![t\log{(0.99356387084)} = \log{\left(\frac{3}{11}\right)}](https://tex.z-dn.net/?f=t%5Clog%7B%280.99356387084%29%7D%20%3D%20%5Clog%7B%5Cleft%28%5Cfrac%7B3%7D%7B11%7D%5Cright%29%7D)
![t = \frac{\log{\left(\frac{3}{11}\right)}}{\log{(0.99356387084)}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%5Cleft%28%5Cfrac%7B3%7D%7B11%7D%5Cright%29%7D%7D%7B%5Clog%7B%280.99356387084%29%7D%7D)
t = 201
There will be only 3 milligrams remaining in the patient's system after 201 minutes.
More can be learned about exponential functions at brainly.com/question/25537936
They always show evolutionary relationships of organisms.
The correct statements regarding a digital storage oscilloscope (DSO) include: d. all are correct statements.
<h3>What is DSO?</h3>
DSO is an abbreviation for digital storage oscilloscope and it can be defined as a type of oscilloscope that is designed and developed to digitally store and analyze the input signal of a waveform, rather than through the use of analog techniques.
In Computer technology, some of the characteristics and features of a digital storage oscilloscope (DSO) include the following:
- DSO is a digitized analog signal.
- DSOs are created by using PCM techniques with Nyquist Sampling rates.
- DSOs primarily is designed to use a bit-depth of 8 bits per sample.
Read more on digital storage oscilloscope here: brainly.com/question/24165789
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Complete Question:
Select the correct statement(s) regarding a DS0.
a. DSO is a digitized analog signal (i.e., typically supporting a 4kHz bandwidth voice signal)
b. DSOs are created using PCM techniques that adhere to Nyquist Sampling rates
c. DSOs use a bit-depth of 8 bits per sample
d. all are correct statements
Almost all students take the PSAT during their junior year, but many students take the PSAT when they are sophomores to get the feel of the test. However, it is only the scores from the PSAT taken in your junior year that are considered for the National Merit Scholarship competition.