Question

Jillana takes a single dose of medication that remains in her body according to the equation r = 200(0.75)d, where r represents the amount of medication remaining after d days. If Jillana had taken the medication four days earlier, the amount of medication remaining in her system relative to the amount that remains in her system after d days would be represented using the equation r2 = 200(0.75)d + 4. Which of the following is an equivalent equation?
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Answer 1

Interpret r = 200(0.75)^d. If taken 4 days earlier the exponent becomes d+4, so

r2 = 200(0.75)^(d+4) = 200(0.75)^d(0.75)^4 = r(0.75)^4.

Numeric: (0.75)^4 = 0.31640625, so r2 = r(0.31640625).