Page 764 - Algebra 1

INVESTIGATION 11
Investigating Exponential Growth and Decay
Water Flow Rates
Water flows from a crack in the side of a swimming
pool, initially releasing one gallon of water. The crack continues to widen as water continues to flow from the pool. For every second after that, the amount flowing from the pool doubles. The table below shows the relationship between time and the amount of water flowing.
Time (s)
Amount of Water (gal)
0
1
1
2
2
4
3
8
Math Reasoning
Analyze What characteristics of the data and the graph indicate that this data does not model a linear function?
1. Create a graph of the data.
2. Predict How many gallons of water flow from the pool in the fourth
second?
Near the origin the graph looks similar to a parabola, however it grows much more quickly. The graph models exponential growth. Exponential growth is
a situation where a quantity always increases by the same percent for a given time period.
Stock Exchange
The annual number of shares S in billions traded on the New York Stock Exchange from 1990 to 2000 can be approximated by the model S = 39(1.2)x, where x is the number of years since 1990.
3. Create a table of values like the one below. Round each share to the nearest billion.
x
S
0
39
2
56
4
6
8
10
Math Reasoning
Analyze In the exponential growth equation f(x) = kbx what is the domain? Why?
Online Connection www.SaxonMathResources.com
4. Plot the coordinates. Connect the points with a smooth curve.
5. Use the graph to estimate the number of shares traded in 1997.
6. Verify Use the equation to calculate the exact number of shares traded in 1997 algebraically.
Investigation 11 749