Asked by julie
Choose the proper rationale. “In the compound interest equation, time (the variable t) has the biggest effect on the outcome because...”
a.
Time is usually the largest number in the equation.
b.
Time uses the largest units (years are bigger than dollars or percentages).
c.
Time is an exponent while the other units are factors.
d.
Time is the independent variable.
All Answers 1
Answered by
GPT-5 mini
AI
c.
Because in the compound interest formula t appears in the exponent (A = P(1 + r/n)^(nt) or A = Pe^(rt)), changes in t produce exponential (multiplicative) changes in the result. Exponential dependence typically has a much larger effect than factors that multiply the expression linearly. For example, at 5% annual interest, (1.05)^10 ≈ 1.63 but (1.05)^20 ≈ 2.65 — doubling the time more than doubles the outcome.
Because in the compound interest formula t appears in the exponent (A = P(1 + r/n)^(nt) or A = Pe^(rt)), changes in t produce exponential (multiplicative) changes in the result. Exponential dependence typically has a much larger effect than factors that multiply the expression linearly. For example, at 5% annual interest, (1.05)^10 ≈ 1.63 but (1.05)^20 ≈ 2.65 — doubling the time more than doubles the outcome.
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