Question

Caffeine takes a certain amount of time to leave your system. if you drink 3 cups of coffee in the morning, the function that represents the amount of caffeine remaining in your body after drinking the coffee is given by g(t)=130(.8246)t where t is time in hours
A. How much caffeine remains in your system after day 1
B. How much caffeine remains in your system after 2 days?

Answer 1

Given:

The function g(t) represents the amount of caffeine remaining in your body after drinking the coffee.

$g(t)=130(.8246)^t$

where t is time in hours.

To find:

The caffeine remains in your system after day 1.

The caffeine remains in your system after day 2.

Solution:

We know that,

1 day = 24 hours.

2 day = 48 hours.

The given function is

$g(t)=130(.8246)^t$

Substitute t=24 in the given function to find the remaining caffeine in the system after day 1.

$g(24)=130(.8246)^{24}$

$g(24)=130(0.00977)$

$g(24)=1.2701$

Therefore, the remains caffeine in your system after day 1 is about 1.2701.

Substitute t=48 in the given function to find the remaining caffeine in the system after day 1.

$g(48)=130(.8246)^{48}$

$g(48)=130(0.000095)$

$g(48)=0.01235$

$g(48)\approx 0.0124$

Therefore, the remains caffeine in your system after day 1 is about 0.0124.