Advanced Math practice question

Answer: A. P = 500 · 2^(t/3)

Doubling means base 2; 'every 3 hours' means the exponent counts how many 3-hour periods have passed, i.e. t/3. Choice B doubles every 1/3 hour — far too fast.

Why the other answers are wrong

B. P = 500 · 2^(3t)

You multiplied t by 3 instead of dividing. The exponent must count how many 3-hour periods have passed, which is t/3 — as written, your function doubles every 1/3 of an hour.

C. P = 500 · 3^(t/2)

You swapped the roles of the two numbers: 2 is the growth factor (doubling) and 3 is the time it takes, so 2 belongs in the base and 3 in the denominator of the exponent.

D. P = 500 + 2^(t/3)

Exponential growth multiplies the starting amount, not adds to it. With addition, 500 barely changes at first and never doubles — it should be 500 · 2^(t/3).

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