Advanced Math practice question

Answer: B. 10

Because 1.331 = 1.1³, f(x) = 3000(1.1³)^(x/12) = 3000(1.1)^(3x/12) = 3000(1.1)^(x/4). Each time x increases by 4, the value is multiplied by 1.1, an increase of 10%, so p = 10 (choice B). Choice D (33.1) misreads the base: 1.331 is the growth factor over 12 months, not over 4 months. Choice C (11.0) divides the 12-month increase of 33.1% by the 3 four-month periods, treating exponential growth as linear instead of taking the cube root of 1.331. Choice A (8.3) divides 33.1% by 4, mistaking the 4 in 'every 4 months' for the number of periods in a year. Only rewriting the base with an exact cube root gives an equivalent function.

Why the other answers are wrong

A. 8.3

You divided the 12-month increase of 33.1% by 4, but 4 is the length of each period in months, not the number of periods — and percent growth can't be split by dividing anyway.

C. 11.0

You divided 33.1% by the 3 four-month periods, which treats the growth as linear; exponential growth requires the cube root of 1.331, which is 1.1, a 10% increase.

D. 33.1

1.331 is the factor over 12 months, not 4; rewrite it as 1.1³ so the function becomes 3000(1.1)^(x/4), showing a 10% increase every 4 months.

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