MS 101 Alg & Trig test two • 14 June 2013 • Name:

Either make the calculation or solve for x as appropriate. Round answers to two decimal places.

1. ____________ e⁰
2. ____________ ln e
3. ____________ log 100
4. ____________ e^x = 20.0856
5. ____________ ln x = 1.60944
6. ____________ log x = 0.90309
7. ____________ 5 ln 8x = 23.22196
8. ____________ $e^{\left(\frac{x}{7}\right)}=20.0856$
9. ____________ ln(2) + ln (17) = ln x
10. ____________ e^x = e⁵⁰ * e⁵
11. ____________ 10^1.949391
12. ____________ ${\log }_{\sqrt{x}}144=2$

The table provides data on world copper production in millions of tons from 1900 to 2010. In the table year 0 is 1900, year 110 is 2010.

Copper is among the most important industrial metals. Copper is used in electrical power cables, data cables, electrical equipment, automobile radiators, cooling and refrigeration tubing, heat exchangers, artillery shell casings, small arms ammunition, water pipes, and jewellery. Copper has been in use at least 10,000 years, but more than 95% of all copper ever mined and smelted has been extracted since 1900. As India and China race to catch up with the West, the copper supply chain is becoming more strained, leading to increased prices and an increase in copper theft. Since copper is a finite resource, at some point in the future new production from within the earth will diminish, and at some earlier time production will reach a maximum. When this will occur is a matter of dispute. Unlike fossil fuels, however, copper is scrapped and reused and it has been estimated that at least 80% of all copper ever mined is still available (having been repeatedly recycled). Wikipedia

Use a spreadsheet to plot the world copper production data. Add an exponential trend line and equation. Note that spreadsheets use the letters "exp" for "e^". For example, exp(2x) means e^(2x).

13. Write the exponential function:
14. ________________ Use the exponential function to calculate the world copper production in the year 120 (that will be 2020).
15. ________________ Use the exponential function to calculate the year in which copper production will be 30 million tons per year.
16. ________________ Copper is a limited resource. The U.S. Geological Survey estimates that there is 950 million tons of copper reserves globally that is economically recoverable. Use the exponential function to calculate the year in which copper production would be 950 million tons per year. (Note that copper could be exhausted prior to the year you calculate because of the production of copper in prior years. A much harder question to answer is what year would 950 million tons of copper be exhausted. One would also have to take into account recycling, the data given here is for copper production and not mining of new ore.)
17. Can copper production keep increasing exponentially without limit? Why or why not?