To model the situation, we can use the exponential function P(t) = 600 * (0.71)^t. After 5 hours, there would be approximately 279.56 mg of ibuprofen in the person's system. It would take approximately 10.29 hours for there to be 30mg of ibuprofen left in their system.
To model the situation, we can use an exponential function. Let P(t) represent the amount of ibuprofen in the person's system at time t. Since the amount of ibuprofen decreases by about 29% each hour, the function can be written as:
P(t) = 600 * (0.71)^t
To find the amount of ibuprofen after 5 hours, we can substitute t = 5 into the function:
P(5) = 600 * (0.71)^5 = 279.56 mg
To find the number of hours it takes for there to be 30mg of ibuprofen left in the system, we can set P(t) equal to 30 and solve for t:
30 = 600 * (0.71)^t. Take the natural logarithm of both sides to solve for t:
ln(30/600) = t * ln(0.71)
t = ln(30/600) / ln(0.71) ≈ 10.29 hours