B Apply

30. Think About a Plan Your friend invested $1000 in an account that pays 6% annual interest. How much interest will your friend have after her college graduation in 4 years?
    • Is an exponential model reasonable for this situation?
    • What equation should you use to model this situation?
    • Is the solution of the equation the final answer to the problem?
31. Oceanography The function y = 20 ( 0.975 ) x y equals 20 . open , 0.975 , close to the x  models the intensity of sunlight beneath the surface of the ocean. The output y represents the percent of surface sunlight intensity that reaches a depth of x feet. The model is accurate from about 20 feet to about 600 feet beneath the surface.
    1. Find the percent of sunlight 50 feet beneath the surface of the ocean.
    2. Find the percent of sunlight at a depth of 370 feet.
32. Population The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 of the animals in the habitat you are studying.
    1. Write a function that models the change in the animal population.
    2. Graphing Calculator Graph the function. Estimate the number of years until the population first drops below 15 animals.

33. Sports While you are waiting for your tennis partner to show up, you drop your tennis ball from 5 feet. Its rebound was approximately 35 inches on the first bounce and 21.5 inches on the second. What exponential function would be a good model for the bouncing ball?

    For each annual rate of change, find the corresponding growth or decay factor.

34. +70%
35. +500%
36. − 75 % negative 75 percent
37. − 55 % negative 55 percent
38. +12.5%
39. − 0.1 % negative 0.1 percent
40. +0.1%
41. +100%

C Challenge

42. Manufacturing The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth $7500. What was the original value of the machine?

43. Zoology Determine which situation best matches the graph.

    

    1. A population of 120 cougars decreases 98.75% yearly.
    2. A population of 120 cougars increases 1.25% yearly.
    3. A population of 115 cougars decreases 1.25% yearly.
    4. A population of 115 cougars decreases 50% yearly.
44. Open-Ended Write a problem that could be modeled with y = 20 ( 1.1 ) x . y equals 20 . open 1.1 close to the x . .

45. Reasoning Which function does the graph represent? Explain. (Each interval represents one unit.)

    

    1. y = ( 1 3 ) 2 x y equals . open , 1 third , close . 2 to the x
    2. y = 2 ( 1 3 ) x y equals 2 . open , 1 third , close to the x
    3. y = − 2 ( 1 3 ) x y equals negative 2 . open , 1 third , close to the x

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