Answer :
Final answer:
The solution is approximately 0.5602 hours or about 33.61 minutes.
Explanation:
To determine how long after drinking one can of Dr.Pepper will only 4mg of caffeine remain in the body, we can use the given function A(x) = 39.4(0.8342)^x.
Let's set up the equation A(x) = 4 and solve for x:
4 = 39.4(0.8342)^x
Divide both sides by 39.4:
0.1015 = (0.8342)^x
Take the logarithm of both sides:
log(0.1015) = x log(0.8342)
Divide both sides by log(0.8342) to solve for x:
x = log(0.1015) / log(0.8342)
Using a calculator, we find that x is approximately 0.5602.
Therefore, it will take approximately 0.5602 hours or about 33.61 minutes for only 4mg of caffeine to remain in the body after drinking one can of Dr.Pepper.
