7
AssignmentMultiple Choice

Vertical Stretches and Shrinks of Exponential Functions

Question 7 • GA-Algebra: Concepts and Connections CR

A patient is given a 50 mg dose of medicine. The medicine's effectiveness decreases every hour at a constant rate of 40%. What is the exponential decay function that models this scenario? How much medicine will be left in the patient's system after 2 hours?

Answer
A
f(x) = 50(0.40)x; 8 mg
B
f(x) = 50(0.60)x; 18 mg
C
f(x) = 50(40)x; 80,000 mg
D
f(x) = 50(60)x; 180,000 mg

Explanation

A 40% decrease each hour means 60% of the medicine remains each hour, so the decay factor is 0.60. Starting with 50 mg, the model is f(x) = 50(0.60)^x. After 2 hours, f(2) = 50(0.60)^2 = 50(0.36) = 18 mg, so the correct choice is B: f(x) = 50(0.60)^x; 18 mg.

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