Question

Use the table to answer the question.



(2 points)
Miguel is planning to invest $5,000. He plans to withdraw his investment and earnings in approximately 10 years. With Option #1, his money will grow according to the function p(x)=5,000(1.06)x
. With Option #2 his money will grow according to the function q(x)=500x+5,000
. He creates sequences for both functions. Which option has the greater rate of change between years 9 and 10? Which option should he choose for his money?

Option #
has the greater rate of change between years 9 and 10. If Miguel plans to invest his money for only 10 years, he should choose Option #

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Answer 1

Option #1 has the greater rate of change between years 9 and 10.

Work:
- Option #1: p(10)-p(9) = 5000(1.06^10 − 1.06^9) = 5000·1.06^9·0.06 ≈ $506.84.
- Option #2: q(10)-q(9) = 500(10)−500(9) = $500.

Since Option #1 increases more over that year, Miguel should choose Option #1.