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Exploring Function Compositions & Circle Areas

Understand function compositions using graphs, analyze ripple radius in a pond, calculate balloon volume changes over time.

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Exploring Function Compositions & Circle Areas

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  1. Compositions of Functions Day 2

  2. Ex 1. Using the graph below, find the following composition of functions.

  3. Ex 2. Using the graph below, find the following composition of functions.

  4. Ex 3

  5. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is r(t) = 0.6t, where t is the time (in seconds) after the pebble strikes the water. The area of the circle is Find and interpret

  6. Ex 4 A spherically shaped balloon is being inflated so that the radius r is changing at the constant rate of 2 in/sec. Find an algebraic representation V(t) for the volume as a function of t and determine the volume of the balloon after 5 seconds.

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