PSAT Math Multiple-Choice Question 148: Answer and Explanation

Question: 148

Month	Balance
0	$1,400
1	$1,344
2	$1,290
3	$1,239
4	$1,189
5	$1,142

The table above shows the balance, in dollars, of a bank account. Which of the following best describes the model that fits the data?

• A. Exponential, decreasing by approximately 4% per month
• B. Exponential, decreasing by approximately 8% per month
• C. Linear, decreasing by approximately $47 per month
• D. Linear, decreasing by approximately $56 per month

Correct Answer: A

Explanation:

A

The question asks for the model that best fits the data. Compare the answer choices. Two choices describe a linear decrease, which is a decrease by the same amount each month, and two choices describe an exponential increase, which is an increase by the same percent each month. Because linear decreases are easier to work with, first determine whether the relationship is linear with a consistent decrease. From month 0 to month 1, the decrease is $1,400 - $1,344 = $56. Eliminate (C), which indicates a decrease of $47. From month 1 to month 2, the decrease is $1,344 - $1,290 = $54. Eliminate (D), since the decrease is not always $56. Therefore, the decrease must be exponential. To find the percent change between months, use the formula . From month 0 to month 1, the percent decrease is . The correct answer is (A).