Question
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) 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?
Answers
GPT 3.5
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.
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.