### 7.2 Exponential Patterns

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• Math Help

According to the National Aquarium, a chambered nautilus is a mollusk, related to the octopus, squid, clam and snail. A nautilus is a cephalopod, which means "head-foot," because its tentacles ("feet") are attached to its head. A newly hatched nautilus feeds on small shrimp and other small prey, while adults feed on crabs, shrimp, and fish, and scavenge on dead animals.

In Example 1, the differences of consecutive volumes are:

The differences are not the same. Also, notice that each difference is greater than the preceding difference, which means the rate of increase is increasing. So, you can conclude that the pattern is not linear. [Recall from Section 7.1 that a sequence of numbers has a linear pattern when each successive number increases (or decreases) by the same amount.]

• Consumer Suggestion

Did you know that a baby Nautilus is about an inch in diameter and has a shell with 7 chambers? As it gets larger, it adds new chambers to its shell.

Check out SeaSky.org, where you can learn about marine life and astronomy, and also play games and read the latest news headlines concerning the sea and sky.

• Checkpoint Solution

A spreadsheet showing the volume for shells with up to 24 chambers is shown below.

The graph curves upward. The vertical difference between consecutive data points increases as the number of chambers increases. This is consistent with the definition of exponential growth; if each successive number increases by the same percent, they will increase by greater and greater amounts.

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```  _____     _____    _    _      ___      _____
/ ____||  |  ___|| | \  / ||   / _ \\   |__  //
/ //---`'  | ||__   |  \/  ||  | / \ ||    / //
\ \\___    | ||__   | .  . ||  | \_/ ||   / //__
\_____||  |_____|| |_|\/|_||   \___//   /_____||
`----`   `-----`  `-`  `-`    `---`    `-----`

```