Advanced MathHardWriting a half-life model
Advanced Math practice question
A patient takes a 60-milligram dose of a medicine. The amount of the medicine in the bloodstream halves every 4 hours. Which function gives the amount A(t), in milligrams, remaining t hours after the dose?
- A. A(t) = 60(1/2)^(t/4)Correct
- B. A(t) = 60(1/2)^(4t)
- C. A(t) = 60(2)^(t/4)
- D. A(t) = 60 − 7.5t
Answer: A. A(t) = 60(1/2)^(t/4)
Each 4-hour period multiplies the amount by 1/2, and t hours contain t/4 such periods. So A(t) = 60(1/2)^(t/4). Check: after 8 hours, 60(1/2)² = 15.
Why the other answers are wrong
- B. A(t) = 60(1/2)^(4t)
- (1/2)^(4t) halves the amount four times every hour — far too fast. It should halve once every 4 hours, so the exponent is t/4.
- C. A(t) = 60(2)^(t/4)
- A base of 2 makes the amount DOUBLE every 4 hours. The medicine is being cleared, so the base is 1/2.
- D. A(t) = 60 − 7.5t
- A linear model loses the same 7.5 mg every hour and reaches zero at 8 hours. Halving is exponential: the amount lost shrinks each period.
More Advanced Math questions
- Hard
A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af… - Hard
How many real solutions does x² + 4x + 5 = 0 have? - Hard
A car worth $20,000 loses 15% of its value each year. What is its value after 2 years? - Hard
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye… - Hard
If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))? - Hard
The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?
Not affiliated with the College Board. SAT is a trademark of the College Board.