Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modelled with the exponential function: f(t) = f(0)ekt where t is the time and k is a constant. Carbon-14 has a half-life of approximately 5730 years. A sample of paper taken from the Dead Sea Scrolls shows that 78.8% of the initial carbon-14 is present. Determine the estimated age of the scrolls. Solve the above problem through the following steps (this applies to your pseudo-code as well as your program): a) declare all known variable for example: • HalfLife=5730 //half-life of Carbon-14 in years • C14 = 78.8/100 //percentage of Carbon-14 in scrolls etc. b) the program first determines the constant k, which is calculated through the following equation: In (0.5) 5730 c) next, the age of the scrolls is calculated by the equation: 78.8 100 k k In( d) finally round the above answer to the nearest year to give the estimated age of the scrolls. e) display the result, which is the estimated age of the dead sea scrolls by using the disp function. Note: your displayed result (answer), needs to be a combination of words and the calculated value.

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Question:
Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modelled with the
exponential function:
f(t) = f(0)ekt
where t is the time and k is a constant. Carbon-14 has a half-life of approximately 5730 years. A sample of paper
taken from the Dead Sea Scrolls shows that 78.8% of the initial carbon-14 is present. Determine the estimated
age of the scrolls.
Solve the above problem through the following steps (this applies to your pseudo-code as well as your program):
a) declare all known variable for example:
• HalfLife=5730 //half-life of Carbon-14 in years
C14 = 78.8/100 //percentage of Carbon-14 in scrolls
etc.
b) the program first determines the constant k, which is calculated through the following equation:
In (0.5)
5730
c) next, the age of the scrolls is calculated by the equation:
78.8.
In 100
k
k
d) finally round the above answer to the nearest year to give the estimated age of the scrolls.
e) display the result, which is the estimated age of the dead sea scrolls by using the disp function. Note:
your displayed result (answer), needs to be a combination of words and the calculated value.
Transcribed Image Text:Question: Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modelled with the exponential function: f(t) = f(0)ekt where t is the time and k is a constant. Carbon-14 has a half-life of approximately 5730 years. A sample of paper taken from the Dead Sea Scrolls shows that 78.8% of the initial carbon-14 is present. Determine the estimated age of the scrolls. Solve the above problem through the following steps (this applies to your pseudo-code as well as your program): a) declare all known variable for example: • HalfLife=5730 //half-life of Carbon-14 in years C14 = 78.8/100 //percentage of Carbon-14 in scrolls etc. b) the program first determines the constant k, which is calculated through the following equation: In (0.5) 5730 c) next, the age of the scrolls is calculated by the equation: 78.8. In 100 k k d) finally round the above answer to the nearest year to give the estimated age of the scrolls. e) display the result, which is the estimated age of the dead sea scrolls by using the disp function. Note: your displayed result (answer), needs to be a combination of words and the calculated value.
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