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Solve a multi-step problem

EXAMPLE 5. Solve a multi-step problem. Forestry. Use the diagram, which illustrates the growth of a giant sequoia, to find the average rate of change in the diameter of the sequoia over time. Then predict the sequoia’s diameter in 2065. Change in diameter. Average rate of change. =.

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Solve a multi-step problem

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  1. EXAMPLE 5 Solve a multi-step problem Forestry Use the diagram, which illustrates the growth of a giant sequoia, to find the average rate of change in the diameter of the sequoia over time. Then predict the sequoia’s diameter in 2065.

  2. Change in diameter Average rate of change = Change in time 141 in. – 137 in. = 2005 – 1965 4 in. = 40 years EXAMPLE 5 Solve a multi-step problem SOLUTION STEP 1 Find the average rate of change. =0.1inch per year

  3. ANSWER In 2065, the diameter of the sequoia will be about 141 + 6 = 147 inches. EXAMPLE 5 Solve a multi-step problem STEP 2 Predict the diameter of the sequoia in 2065. Find the number of years from 2005 to 2065. Multiply this number by the average rate of change to find the total increase in diameter during the period 2005–2065. Number of years = 2065 – 2005 =60 Increase in diameter =(60years) (0.1inch/year) = 6 inches

  4. for Example 5 GUIDED PRACTICE GUIDED PRACTICE 13.What If ? In Example5, suppose that the diameter of the sequoia is 248 inches in 1965 and 251 inches in 2005. Find the average rate of change in the diameter, and use it to predict the diameter in 2105.

  5. Change in diameter Average rate of change = Change in time 251 in. – 248 in. = 2005 – 1965 3 in. = 40 years for Example 5 GUIDED PRACTICE SOLUTION STEP 1 Find the average rate of change. =0.075inch per year

  6. ANSWER In 2105, the diameter of the sequoia will be about 251 + 7.5 = 258.5 inches. for Example 5 GUIDED PRACTICE STEP 2 Predict the diameter of the sequoia in 2105. Find the number of years from 2005 to 2105. Multiply this number by the average rate of change to find the total increase in diameter during the period 2005–2105. Number of years = 2105 – 2005 =100 Increase in diameter =(100years) (0.075inch/year) =7.5inches

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