A adult takes 600mg of ibuprofen. Each hour, the amount of ibuprofen in the person's system decreases by about 29%.
a) Write an exponential function to model this situation.
b)About how much ibuprofen would be in the person's system after 5 hours?
c)After about how many hours would there be 30mg of ibuprofen left in their system?
a) The exponential function to model this situation can be written as:
f(t) = 600 * (1 - 0.29)^t, where t represents the number of hours.
b) To determine how much ibuprofen would be in the person's system after 5 hours, we can substitute t = 5 into the exponential function:
f(5) = 600 * (1 - 0.29)^5
Using a calculator, we can evaluate this expression to find that approximately 129.06mg of ibuprofen would be in the person's system after 5 hours.
c) To determine the number of hours it would take for there to be 30mg of ibuprofen left in the person's system, we need to solve the exponential function for t:
30 = 600 * (1 - 0.29)^t
Dividing both sides of the equation by 600 and taking the logarithm of both sides, we can solve for t:
log((1 - 0.29)^t) = log(30/600)
t * log(0.71) = log(0.05)
t = log(0.05) / log(0.71)
Using a calculator, we can evaluate this equation to find that approximately t ≈ 14.98 hours. Thus, after about 15 hours, there would be 30mg of ibuprofen left in their system.