Use the image to answer the question.

Question

A coordinate plane's x-axis ranges from negative 1 to 4 by increments of 1 and is labeled Time with decade as the units. The y-axis ranges from 0 to 10,000 by increments of 1,000 and is labeled Current Balance with dollar as the units. A solid curve is plotted.

The graph shows the total amount of an investment account with a principal of $1,500 which increases 1.5 times every 10 years. Use the graph to estimate the total amount of the account if $1,500 is invested for 32 years.

(1 point)
Responses

$5,000
$5,000

$6,200
$6,200

$5,500
$5,500

$7,800

Answer 1

To estimate the total amount of the investment after 32 years, we can determine how many 10-year increments fit into 32 years.

32 years includes three full 10-year increments (30 years) plus an additional 2 years.

The investment grows by 1.5 times every 10 years. Thus, after 30 years (3 increments):

• Initial amount: $1,500
• After 10 years: $1,500 × 1.5 = $2,250
• After 20 years: $2,250 × 1.5 = $3,375
• After 30 years: $3,375 × 1.5 = $5,062.50

Now, for the two additional years, we need to estimate growth. Since we only have information for complete 10-year increments, we'll assume that the growth will be linear within this period, as the exact curve isn't provided.

We know the investment reaches about $5,062.50 after 30 years when it increases to $5,062.50 from $3,375 in the first ten years and again by 1.5 times in the next 10 years.

Due to the graph being solid (exponential growth curve), we can reasonably estimate that the amount will increase a bit in the following 2 years. Assuming a modest linear increase (in a rough estimation) could put the amount at around $5,500 at 32 years.

So, the closest estimate would be $5,500.