Note: Use the information below to answer each part of the question, and show all necessary work. You can type or upload your work in the space provided.
An adult takes 600 mg 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. (2 pts)
b) About how much ibuprofen would be in the person's system after 5 hours? (2 pts)
c) After about how many hours would there be 30mg of ibuprofen left in their system? (3 pts)
a) The exponential function to model this situation is:
f(x) = 600 * (0.71)^x
b) To find out how much ibuprofen would be in the person's system after 5 hours, we can substitute x = 5 into the exponential function:
f(5) = 600 * (0.71)^5
f(5) = 600 * 0.1681
f(5) ≈ 100.86 mg
Approximately 100.86 mg of ibuprofen would be in the person's system after 5 hours.
c) To find out after about how many hours there would be 30 mg of ibuprofen left in their system, we can set the exponential function equal to 30 and solve for x:
30 = 600 * (0.71)^x
Dividing both sides by 600 gives:
0.05 = 0.71^x
Taking the logarithm (base 0.71) of both sides gives:
log(0.05) = log(0.71^x)
Using the logarithmic property log(a^b) = b * log(a), we can rewrite the equation as:
log(0.05) = x * log(0.71)
Using a calculator to evaluate both sides, we find:
x ≈ 19.97
After about 19.97 hours, there would be approximately 30 mg of ibuprofen left in their system.