Advanced MathHardExponential growth modeling
Advanced Math practice question
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t years?
- A. 1000(0.06)^t
- B. 1000(1.06)^tCorrect
- C. 1000(6)^t
- D. 1000 + (1.06)^t
Answer: B. 1000(1.06)^t
Growing 6% per year means each year the value is multiplied by 1 + 0.06 = 1.06, giving 1000(1.06)^t. The trap is choice A, using 0.06 as the growth factor — that would shrink the investment by 94% each year instead of growing it.
Why the other answers are wrong
- A. 1000(0.06)^t
- You used 0.06 as the multiplier, which would leave only 6% of the money each year; growing by 6% means multiplying by 1 + 0.06 = 1.06.
- C. 1000(6)^t
- You read "6%" as the number 6, so this multiplies the investment by 6 each year — a 500% annual increase rather than 6%.
- D. 1000 + (1.06)^t
- Compound growth multiplies the principal each year rather than adding to it; the 1000 must be a factor, not a separate added term.
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