Exponents and Compound Interest

qian58
6 days ago
2 min read

Once you know a handful of rules, exponent questions become fast, reliable points. Compound interest is on almost every exam.

The Regents tests exponent rules — multiplying powers, raising a power to a power — and exponential growth, which is what happens when something multiplies by a constant rate each period. Compound interest is the classic example.

Click here for some tips on exponents and compound interest

Rules worth knowing

xᵃ × xᵇ = x^(a+b) (multiply → add exponents)
(xᵃ)ᵇ = x^(a×b) (power of a power → multiply exponents)
(xy)ⁿ = xⁿ × yⁿ (distribute the exponent)
Compound interest: A = P × (1 + r)^t
P = starting amount, r = rate as a decimal, t = time

⚠3% as a decimal is 0.03 — not 0.3. Move the decimal point two places left. Then the growth factor is 1 + 0.03 = 1.03. Confusing 3% with 30% is one of the most common errors on every Regents.

Worked example

Problem: A population of bacteria doubles every hour starting from 500. Which equation gives the population y after x hours?

(1) y = 500 + 2x (2) y = 500 × 2^x (3) y = 2 × 500^x

Try it yourself! Below is a real Regents problem from January 2024

Problem: Joe deposits $4,000 into a CD earning 3% interest compounded annually. Which equation gives the value y after x years? (1) y = 4000 + 0.3x (2) y = 4000 + 0.03x (3) y = 4000 × (1.3)^x (4) y = 4000 × (1.03)^x

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