Question

How does the graph of the explicit form of the sequence for Maurice's money market account balance while he attended graduate school compare to the graph of the recursive form?

Option 1: The explicit form graph is a straight line, while the recursive form graph shows exponential growth.
Option 2: The explicit form graph displays gradual growth, while the recursive form graph has abrupt fluctuations.
Option 3: The explicit form graph depicts consistent growth, whereas the recursive form graph shows irregular patterns.
Option 4: The explicit form graph is erratic, while the recursive form graph represents steady financial progress.

Answer 1

Option 1 is correct; the explicit form of Maurice's money account balance would graph as a straight line, indicating constant growth, whereas the recursive form would show exponential growth due to the principles of compound interest.

Step-by-step explanation:

When comparing the graph of the explicit form of the sequence for Maurice's money market account balance to the graph of the recursive form, it's important to understand the nature of growth in each case. The explicit form of a sequence, when representing financial growth such as interest, generally shows a predictable, consistent pattern, often linear or exponential depending on the formula used. In contrast, the recursive form, particularly in the context of compound interest, is built on the principle that growth builds upon the previous total, including earned interest, leading to exponential growth.

Option 1 seems to be the correct answer here, as the explicit form which is generally a straightforward algebraic expression would graph as a straight line, demonstrating a fixed growth rate. Meanwhile, the recursive form, reflecting compound interest, would display exponential growth on the graph as the growth builds upon itself each period.

The information provided illustrates that to maintain a consistent growth rate, the nominal change (like a $2 raise) must increase each time, because as the base amount grows, the same nominal increase represents a smaller percentage change. This is consistent with principles of compound growth, where the base includes past growth, leading to a cumulative increase over time.