Question

Use the image to answer the question.

A coordinate plane has an increasing solid curve and a dotted straight line plotted on it.
▼Click for Long Desc
The x-axis shows values from negative 4 to 40 marked in increments of 2, but labeled in increments of 4. The y-axis shows values from 0 to 40,000 in increments of 5,000. A solid curve with a bi-directional arrow passes through left parenthesis 0 comma 5,000 right parenthesis, left parenthesis 12 comma 10,000 right parenthesis, left parenthesis 24 comma 20,000 right parenthesis, left parenthesis 32 comma 32,500 right parenthesis, and left parenthesis 35 comma 40,000 right parenthesis. A dotted straight line with a bi-directional arrow passes through left parenthesis 0 comma 5,000 right parenthesis, left parenthesis 10 comma 10,000 right parenthesis, left parenthesis 20 comma 15,000 right parenthesis, left parenthesis 30 comma 20,000 right parenthesis, and left parenthesis 40 comma 25,000 right parenthesis. The line and the curve intersect at two points: left parenthesis 0 comma 5000 right parenthesis, and left parenthesis 17 comma 13,500 right parenthesis. All coordinate values are approximate and the coordinates are unlabeled.


Given that the graph q(x)
is linear and the graph p(x)
is exponential, solve the following problem:

Juan is planning to invest $5,000. 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 decides to graph both functions. What does he observe from the graph?

(1 point)
For the first 10 years, Juan’s money will grow faster with Option #
, but after that it will grow faster with Option #
.

Answer 1

For x = 10: p(10) = 5000(1.06)^10 ≈ 8954 and q(10) = 500(10)+5000 = 10000, so Option #2 is larger at 10 years. The graphs intersect later (around x = 17), after which the exponential p(x) grows faster.

Answer: For the first 10 years, Option #2; after that, Option #1.