Question

Rosa has a headache and takes 600 mg of Tylenol. The amount, A, of Tylenol remaining in her body after n hours is given by the formula A = 600 * (0.78)^n. How much of the Tylenol remains in her body after 5 hours? Round your answer to the nearest hundredth.

a) Rosa will have 349.92 mg of Tylenol remaining in her body after 5 hours.
b) Rosa will have 420.00 mg of Tylenol remaining in her body after 5 hours.
c) Rosa will have 408.33 mg of Tylenol remaining in her body after 5 hours.
d) Rosa will have 388.80 mg of Tylenol remaining in her body after 5 hours.

Answer 1

After 5 hours, none of the provided options match the calculated value. Using the decay formula A = 600 * (0.78)^5, Rosa will have approximately 172.86 mg of Tylenol remaining in her body, which is not listed in the given choices.

Step-by-step explanation:

Rosa has a headache and takes 600 mg of Tylenol. The amount, A, of Tylenol remaining in her body after n hours is given by the formula A = 600 \* (0.78)^n. To find out how much of the Tylenol remains in her body after 5 hours, we substitute n with 5:

A = 600 \* (0.78)^5

Calculating this using a calculator gives us:

A ≈ 600 \* 0.2881 ≈ 172.86 mg

Therefore, none of the options given (a) 349.92 mg, (b) 420.00 mg, (c) 408.33 mg, or (d) 388.80 mg, are correct. After 5 hours, Rosa will have approximately 172.86 mg of Tylenol remaining in her body, which is not listed in the options provided.