Question

Use the table to answer the question.

This table compares two investment options over a 10-year period.
Term Number 1 2 3 4 5 6 7 8 9 10
Sequence for
Option #1 5,300 5,618 5,955.1 6,312.4 6,691.1 7,092.6 7,518.2 7,969.2 8,447.4 8,954.2
Sequence for
Option #2 5,500 6,000 6,500 7,000 7,500 8,000 8,500 9,000 9,500 10,000
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⋅1.06x
. 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?

(1 point)
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 #
.

Answer 1

Option #1 has the greater rate of change between years 9 and 10 (8954.2 − 8447.4 = 506.8 vs. 500). If Miguel plans to invest for only 10 years, he should choose Option #2 (ends with $10,000 vs. about $8,954.20).