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Worksheet 2 |
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Worksheet 2 |
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Exponential Modeling
1. U.S. Population Growth – The 2000 census found a U.S. population of about 281 million. Write an equation for the U.S. population that assumes exponential growth at 0.7% per year.
a. Use the equation to predict the U.S. population in 2100.
b. Use Excel to predict the U.S. population in 2100.
2. Human vs Black Bear Population - The New York Times reported that wildlife biologists have found a direct link between the increase in the human population in Florida and the decline of the local black bear population. From 1953 to 1993, the human population increased, on average, at a rate of 8% per year, while the black bear population decreased at a rate of 6% per year. In 1953 the black bear population was 11,000. In 1993 the human population of Florida was 13 million.
a. Find the black bear population for 1993.
b. If this trend continues, when will the black bear population be less than 100?
c. If the human population trend continues, how long will it take the human population to double?
Radioisotope Dating
Exponential decay occurs with radioactive substances. This fact can help scientists estimate the age of objects. All living creatures contain carbon. Some of that carbon is in the form of radioactive Carbon-14. Since it is radioactive, carbon-14 decays. This substance decays fairly slowly; it decreases by approximately 1.202% every 100 years. If an archeologist unearthed a fossil of a once living creature, the amount of carbon-14 remaining in that fossil would help the archeologist calculate the number of years since the creature died. This is called carbon dating.
If a fossil contained 75% of the original carbon-14, how old is the fossil?
Solving with Logarithms
To get a more exact answer to the question above, you can use the equation of the function and solve for time. Start with the equation: y = 100 * (1-.01202)x where, y is the percent of carbon-14 remaining in the fossil and x is the number of 100 year increments that have passed since the creature died.
Plug in 75 for y: 75 = 100 * (1-.01202)x
Solve using logarithms:
Since x is the number of 100 year increments, we need to multiply the answer by 100 to get the number of years since the creature died.
