Unit 9, Lesson 3
Representing Exponential Growth
Integrated Math 1
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Refer back to your work in the table of the previous task. Use that information and the given coordinate planes to graph the following:
a. Graph
b. Graph
In relationships where the change is exponential, a quantity is repeatedly multiplied by the same amount. The multiplier is called the growth factor.
Suppose a population of cells starts at 500 and triples every day. The number of cells each day can be calculated as follows:
| number of days | number of cells |
|---|---|
| 0 | 500 |
| 1 | 1,500 (or |
| 2 | 4,500 (or |
| 3 | 13,500 (or |
We can see that the number of cells (
The equation can be used to find the population on any day, including day 0, when the population was first measured. On day 0, the population is
Here is a graph of the daily cell population. The point
Graph of an exponential function, origin O. Horizontal axis, number days, scale 0 to 4, by 1’s Vertical axis, cell population, scale 0 to 20,000, by 5,000’s. The function is discrete and has these points: (0 comma 500), (1 comma 1,500), (2 comma 4,500) and (3 comma 13,500).
Each point is 3 times higher on the graph than the previous point.
In an exponential function, the output is multiplied by the same factor every time the input increases by 1. This multiplier is called the growth factor.