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riadik2000 [5.3K]
3 years ago
13

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the bod

y t hours later is given by A(t) = 10(0.7)t and that in order for the drug to be effective, at least 4 milligrams must be in the body.
a. Determine when 2 milligrams is left in the body.
b. What is the half-life of the drug?
Mathematics
1 answer:
adell [148]3 years ago
6 0

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

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3 years ago
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You and your friend each collect rocks and fessis your friend collects three times as many roots and half as many fossils as you
n200080 [17]

Answer:

Number of rocks and fossils collected by you is <u>1 and  24</u> respectively

Number of rocks and fossils collected by your friend is <u>3 and 12 </u>respectively

Step-by-step explanation:

Let  the number of Rocks you collect be x

Let  the number of Fossils you collect be y

Then the total number pf objects you collected will be

x + y = 25

x = 25 - y------------------------------(1)

Your friend collects three times as many rocks and half as many fossils as you.

This can be written as

3x + y (1/2) = 15

3x + (y/2) = 15-------------------(2)

Substituting (1) in (2)

3(25 - y) + (y/2) = 15

75 - 3y + (y/2) = 15

Grouping the like terms we get,

75 - 15 = 3y = (y/2)

60 = ( 6y - y /2)

60 x 2 = 6y -y

120 = 5y

y = 120/5

y = 24

Substituting  y value in equation(1) we get

x = 25 - 24

x= 1

y= 24

Friends collects 3 times rock

so collects 3x =3(1) = 3rocks

Also he collects half as many fossils

That is

y/2 = 24/2 = 12 fossils

<u><em>Hope this help you! :)</em></u>

5 0
2 years ago
To some Marines one cruising at 25 kn in the other 20 kn left the naval base at the same moment. Three hours later they were 100
Rus_ich [418]
I believe you would have to multiply both 25 and 20 and what ever number you get dived by 100 if the numbers to high multiply aging or subtract the number (if it's wrong I'm really not good at my math I'm sorry)
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3 years ago
Jean can pack 5 cartons in 15 minutes. Which expression can be used to show the number of cartons Jean can pack in x hours? Grou
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Answer: 20x

Step-by-step explanation:

First we should note that 60 minutes = 1 hour. Therefore, 15 minutes = 15/60 = 1/4 hour

Since Jean can pack 5 cartons in 1/4 hours, the number of carton that he can pack in one hour will be:

= 5 ÷ 1/4

= 5 × 4

= 20 cartons.

Therefore, to get the number of cartons that Jean can pack in x hours, we will multiply 20 by x. This will be:

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6 0
2 years ago
Paid for $22 for for movie tickets how many would they have pay for for 16 tickets
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Answer:

$352

Step-by-step explanation:

One ticket costs $22, so 16 tickets would be 22 times 16.

Final Answer: $352

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