Each year, the value of an investment increases by 2% of its current value. Which of the following functions best...

1. TRANSLATE the problem information

• Given information:
  • Investment increases by 2% of its current value each year
  • Need to identify the function type that models this growth
• What this tells us: The growth amount changes each year because it's based on the current value, not the original amount

2. INFER what type of growth this represents

• Since the increase is "2% of current value," the amount added gets larger each year
• This is compound growth, not simple linear growth
• Each year, we multiply by \(\mathrm{(1 + 0.02) = 1.02}\)

3. INFER the mathematical pattern

• Year 0: \(\mathrm{V_0}\) (original value)
• Year 1: \(\mathrm{V_0 \times 1.02}\)
• Year 2: \(\mathrm{V_0 \times 1.02 \times 1.02 = V_0 \times (1.02)^2}\)
• Year t: \(\mathrm{V_0 \times (1.02)^t}\)

4. INFER the function characteristics

• This creates the exponential function \(\mathrm{V(t) = V_0(1.02)^t}\)
• Since the base \(\mathrm{1.02 \gt 1}\), the function increases over time
• This is an increasing exponential function

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misinterpret "increases by 2%" as adding the same amount each year (linear growth) rather than recognizing compound growth.

They think: "2% increase each year means we add a constant amount each year, so this must be linear growth." They don't realize that 2% of the current value means the actual dollar amount increases each year.

This may lead them to select Choice (D) (Increasing linear).

Second Most Common Error:

Conceptual confusion about exponential vs linear: Students know the value increases but can't distinguish between exponential and linear growth patterns.

They recognize it's increasing but guess between the two increasing options without understanding the mathematical difference between constant addition (linear) and constant multiplication (exponential).

This leads to confusion and random selection between choices C and D.

The Bottom Line:

This problem tests whether students understand that compound growth (percentage of current value) always creates exponential functions, while simple growth (constant amounts) creates linear functions. The key insight is recognizing what "2% of current value" truly means mathematically.