# Reading a point from a curve or line

*Practice Problems*

The problems below walk you through the steps for reading points from a line. You can click on any of the graphs to open a bigger version or you can click the link under the graph to download a pdf of the graph for printing! Please try to complete these activities without peeking at the answers - this will help you when you get to the quiz at the end!## Radioactive Decay and Radiometric Dating

Geologists use information about the ratio of radioactive (parent) atoms to their decay product (daughter) atoms to understand the age of igneous, metamorphic and sedimentary rocks. The behavior of all radioactive elements is the same and the time it takes for one-half of the parent atoms to decay to daughter atoms is called the half-life. The graph below shows a plot of Daughter/Parent Ratio to Half-lives elapsed showing how geologists use isotopes to determine the age of rocks. This is a general plot that works for any isotope system. Use this plot to answer the questions below about reading points from a line.

Click to enlarge, or download a PDF (Acrobat (PDF) 25kB Jun25 10)

**Question 1: Using the isotope plot above, determine the number of half-lives elapsed when the Daughter/Parent Ratio is 20.**

**Question 2: Using the same isotope plot above, determine the Daughter/parent ratio when 5.5 half-lives have elapsed.**

## Floods and Flood Frequency

Geologists keep track of the "stage" or height of floods every year and use that data to predict the probability that a flood will occur in any given year. The plot below is called a flood frequency curve, constructed from data collected over a number of years (sometimes as many as 100 -200 years. The plot below represents data from a hypothetical river for which we had 69 years of data. The probability is reported as something called a Recurrence interval and is reported in "years". Use the plot below to answer the following questions. Click to enlarge or you can download a PDF version to print (Acrobat (PDF) 53kB Jun25 10).

### Question 1: Determine the flood stage for a flood with a recurrence interval of 400 years.

### Question 2: Determine the recurrence interval for a flood stage of 38 feet.

## Climate Change and Greenhouse Gases

Geoscientists use information gathered from the atmosphere and ice cores to understand long-term climate change and the role of greenhouse gases. On top of Mauna Loa, in Hawaii, a weather station collects information about the CO_{2}content of our atmosphere - Mauna Loa is far above the immediate influence of CO

_{2}emissions from traffic because it is nearly 4170 meters (about 13680 feet) above sea level (see USGS Mauna Loa Volcano). The data collected between 1987 and 2006 is presented below in graphical form. Use this graph (you can download a larger version as a PDF to print) to answer the questions below. Note that the data shows a cyclical pattern that is associated with seasons (e.g., winter and summer) but that the trend shows that CO

_{2}concentrations in our atmosphere are generally increasing.

Click to enlarge or you can download a PDF version to print (Acrobat (PDF) 43kB Jun28 10).

### Question 1: What was the concentration of CO_{2} at Mauna Loa in January of the year 2000?

### Question 2: Determine what dates in the last 10 years (of record) showed that carbon dioxide concentrations were equal to 350 ppm.

## Next Steps

If you still need help, you can go back to the explanation page or look at some of the links below.

## Need more practice?

**VisionLearning**has some problems where you can practice with graphs and reading information from the lines on them.