Answer:
the maximum concentration of the antibiotic during the first 12 hours is 1.185
at t= 2 hours.
Step-by-step explanation:
We are given the following information:
After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in 

Thus, we are given the time interval [0,12] for t.
- We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
- The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.
First, we differentiate C(t) with respect to t, to get,

Equating the first derivative to zero, we get,

Solving, we get,

At t = 0

At t = 2

At t = 12

Thus, the maximum concentration of the antibiotic during the first 12 hours is 1.185
at t= 2 hours.
Answer:

Step-by-step explanation:

Expand with the distributive rule:


Add 4/3 to both sides:

Subtract 4x from both sides



So, if it grows by 6.75%, each year the population is 106.75% of the year before.
After 1 year, 370,000(1.0675). After two years, 370,000(1.0675)(1.0675).
370,000(1.0675)12 = your answer
Answer:
314 million
Step-by-step explanation:
Given that :
Number of motor vehicle in the U.S for every 1000 people = 828
If the number of motor vehicle in the United States = 260 million
Then,
Let x = number of people Given number of vehicles = 260,000,000
1000 people = 828 vehicles
x = 260,000,000
828x = (260,000,000 * 1000)
828x = 260,000,000,000
x = 314009661. 835
x = 314 million (approx)
Let's calculate each area.
4 m:
We need to divide it by 2 to find the radius.
4÷2=2
Now let's put it in the formula.
2²π
4π=12.5663706≈13
6 m:
We need to divide it by 2 for the radius.
6÷2=3
Now put it in the formula.
3²π
9π=28.2743≈28
Now subtract 13 from 28.
28-13=15
So, the difference between their area is 15 m².