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The answers to most of the following exercises are in terms of logarithms and exponentials. A calculator can be helpful, enabling you to express the answers in decimal form.The frozen remains of a young Incan woman were discovered by archeologist Johan Reinhard on Mt. Ampato in Peru during an expedition in $1995 .$a. How much of the original carbon- 14 was present if the estimated age of the "Ice Maiden" was 500 years?b. If a $1 \%$ error can occur in the carbon- 14 measurement, whatis the oldest possible age for the Ice Maiden?

a.) About $ 94.1 \% $ left. b.) At max 505 years old, in 1995.

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

Integrals and Transcendental Functions

Section 2

Exponential Change and Separable Differential Equations

Functions

Trig Integrals

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So in 1995 there was exponentially in in Peru that found what is called the ice maiden in, um, and they estimate the age to be 500 years. They want to determine about how much of carbon 14 was left. So now, in example, five they tell us for C 14 dating that are constant. K is natural aga to over 5730 reciprocal years, and this falls exponential decay since it's radioactive. So if we want to find how much was left after 500 years, we would just do why of 500 and plug all of that. And so it's going to be why not times e to the negative? It's all right. This has 500 natural log of two over 5730 which should give us approximately. Let's see so negative 500 times. Natural log of two is about negative 346. Divide that by 5730 was about negative 0.6. So why not times E to the negative 0.6 now exponentially ating? That should give about 0.941 AB zero point 941 Why not? Which that is going to imply. Then about 94 point A 4.1% left, and that was in 1995. Now they tell us if there is about 1% error in this process, what is actual maximum age? All right, well, they tell us, is about 500 years. So to find Max age, we would just multiply Bye one plus our error percent, which I'll call just e. Actually, that's probably bad number. Let's use our sub e and we would just multiply by our H, so we'd end up with 1.1 times. Well, they said it was about 500 years, so we would expect adding Max an age of 505 years. And so this was in 1995 when they actually found it.

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