Question

one 12 oz can of Dr.Pepper contains about 39.4 mg of caffeine. The function A(x)=39.4(0.8342)^x Determine how long after drinking one can of Dr.Pepper will only 4mg of caffeine remain in the body?

Answer 1

The solution is approximately 0.5602 hours or about 33.61 minutes.

Step-by-step 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.