Jillana takes a single dose of medication that remains in her body according to the equation r is equal to 200 times 0 point 7 5 to the d th power , where r represents the amount of medication remaining after d days. If Jillana had taken the medication two 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 r sub 2 is equal to 200 times 0 point 7 5 raised to the d plus 2 power Which of the following is an equivalent equation?
Answer
A
r sub 2 is equal to 632 point 1 0 times 0 point 7 5 to the d th power
B
r sub 2 is equal to 112 point 5 times 0 point 7 5 to the d th power
C
r sub 2 is equal to 200 point 3 2 times 0 point 7 5 to the d th power
D
r sub 2 is equal to 199 point 6 8 times 0 point 7 5 to the d th power
Explanation
Use the exponent rule to split the power: 0.75^(d + 2) = 0.75^d × 0.75^2. Since 0.75^2 = 0.5625, the coefficient becomes 200 × 0.5625 = 112.5. So the equivalent equation is r₂ = 112.5 × 0.75^d, choice B.
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