Respuesta :
Given:
The function g(t) represents the amount of caffeine remaining in your body after drinking the coffee.
[tex]g(t)=130(.8246)^t[/tex]
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
[tex]g(t)=130(.8246)^t[/tex]
Substitute t=24 in the given function to find the remaining caffeine in the system after day 1.
[tex]g(24)=130(.8246)^{24}[/tex]
[tex]g(24)=130(0.00977)[/tex]
[tex]g(24)=1.2701[/tex]
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.
[tex]g(48)=130(.8246)^{48}[/tex]
[tex]g(48)=130(0.000095)[/tex]
[tex]g(48)=0.01235[/tex]
[tex]g(48)\approx 0.0124[/tex]
Therefore, the remains caffeine in your system after day 1 is about 0.0124.
Answer: for one day, it’s 0.0124
Step-by-step explanation:1d=24h
g(24)
