Find x in the equation: (5^x)^3=5^1

At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given

Nostrana [21]

Answer:

a. The initial amount was 10 mg.

b. The percentage of the drug leaving the body each hour is 0.18, this is 18% per hour.

c. The amount of drug that remains in the body 6 hours after dosing is 3.04 mg.

d. The time until only 1 mg of the drug remains in the body is 11.6 hours.

Step-by-step explanation:

You know that at time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by :

$A=10*(0.82)^{t}$

a. The initial quantity occurs when time t is the initial t, that is, t is equal to 0. Then:

$A=10*(0.82)^{t}=10*(0.82)^{0}=10*1\\$

A=10

The initial amount was 10 mg.

b. Considering that an exponential growth is determined by:

$A=A0*(1-r)^{t}$ , where A is the amount after a certain number of a certain time, Ao is the initial amount, r is the rate and t is the time, so the percentage of the drug that leaves the body each hour is :

1-r=0.82

Solving:

1-r -1= 0.82 -1

-r= -0.18

r= 0.18

The percentage of the drug leaving the body each hour is 0.18, this is 18% per hour.

c. The amount of drug that remains in the body 6 hours after dosing is when t = 6:

$A=10*(0.82)^{6}$

Solving:

A= 3.04 mg

The amount of drug that remains in the body 6 hours after dosing is 3.04 mg.

d. The time that passes until only 1 mg of the drug remains in the body is calculated taking into account that A = 1 mg:

$1=10*(0.82)^{t}$

Solving:

$0.1=(0.82)^{t}$

㏒ 0.1= t*㏒ 0.82

㏒ 0.1 ÷ ㏒ 0.82= t

11.6 hours= t

The time until only 1 mg of the drug remains in the body is 11.6 hours.

4 0

3 years ago

Find the inverse of the function. y = 5x + 5

Ugo [173]

Answer:

f^−1(x)=x/5 −1

Step-by-step explanation:

8 0

3 years ago

A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great

ElenaW [278]

The length of an arc can be related to the radius of circle and the angle it makes at the center of the circle by following equation:

s = rФ

Radius is given to be = 3960 miles
We are to find the arc length in feet, so we convert the miles to feet.
1 mile = 5280 feet.
So,
Radius = 3960 x 5280 feet = 20908800 feet
Angle = 1/60 degree
The angle must be in radians before, we use its value in the equation given above.

So, 1/60 degrees in radians will be:

$\frac{1}{60} * \frac{ \pi }{180} = \frac{ \pi }{10800}$

Now we can use this value of angle in above equation to find the arc length. $s = 20908800 * \frac{ \pi }{10800} = 6080 feet$

So, rounded of to nearest 10 feet, the length of one nautical mile is 6080 feet.

6 0

4 years ago

Read 2 more answers

Marica purchase three doughnuts for 2 dollers each the cashier told her when you buy 2 donuts, you get the third one half price

insens350 [35]

What's the question?

6 0

3 years ago

A box is contructed out of two different types of metal. the metal for the top and bottom, which are both square, costs $3 per s

zysi [14]

Let x ft be the length of the base square and y ft be the height of the box.

The volume of the box is

$V=x\cdot x\cdot y\ ft^3.$

Since the box has a volume of 15 cubic feet, then

$x^2y=15,\\ \\y=\dfrac{15}{x^2}.$

You need to construct two squares from the metal that cost $3 per square foot.

The area of each square is $x^2\ ft^2$ and the total cost for these two squares is $2\cdot x^2\cdot 3=6x^2.$

The area of each side face is $x\cdot y=x\cdot \dfrac{15}{x^2}=\dfrac{15}{x}.$ Then the total cost for sides is $4\cdot \dfrac{15}{x}\cdot 10=\dfrac{600}{x}.$