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4 years ago

After a certain medicine is ingested, its concentration in the bloodstream changes over time.

Mathematics

2 answers:

myrzilka [38]4 years ago

8 0

Answer:

Every hour, the medicine concentration decays by a factor of 4%.

Step-by-step explanation:

The relationship between the elapsed time, t, in minutes, since the medicine was ingested, and its concentration in the bloodstream, C (t), is:

$C(t)=61\cdot (0.96)^{t}$

The decay function is:

$y=a(1-r)^{t}$

Here,

y = final amount

a = initial amount

r = decay rate

t = time

From the provided expression the decay rate is:

$1-r=0.96\\r=1-0.96\\r=0.04$

Thus, every hour, the medicine concentration decays by a factor of 4%.

Mashcka [7]4 years ago

7 0

Answer:

0.09

Step-by-step explanation:

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Given that 4(n-5)+2=3(n-1),what is the value of n

Alina [70]

We'll first simplify both sides of the expression to get (simply using the distributive property):
$4n-20+2=3n-3$

Then, we can simplify a little bit:
$4n-18 = 3n-3$

To solve for n, we have to isolate it. Let's subtract 3n from both sides to further simplify it:
$n-18 = -3$

Then, add 18 to both sides to get the value of n:
$n = 15$

And that's your answer. If you have questions on how I got that, feel free to ask!

5 0

3 years ago

Read 2 more answers

You have 24 months left until you graduate and you plan on buying yourself a new $20,000 car on graduation day. If you invest $3

shusha [124]

Answer: No, the money won't be enough to buy the car

Step-by-step explanation:

you plan on buying yourself a new $20,000 car on graduation day and graduation day is 24 months time. If you invest $300 a month for the next 24 months.

The principal amount, p = 300

He is earning 4% a month, it means that it was compounded once in four months. This also means that it was compounded quarterly. So

n = 4

The rate at which the principal was compounded is 4%. So

r = 4/100 = 0.04

It was compounded for a total of 24 months. This is equivalent to 2 years. So

n = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount that would be compounded at the end of n years.

A = 300(1 + (0.04/4)/4)^4×2

A = 300(1 + 0.01)^8

A = 300(1.01)^8

A = $324.857

The total amount at the end of 24 months is below the cost of the car which is $20000. So he won't have enough money to buy the car

3 0

4 years ago

A gas station stands at the intersection of a north-south road and an east-west road. A police car is traveling toward the gas s

DanielleElmas [232]

Answer:

a)DL/dt is positive then L s increasing

b) L still increasing

Step-by-step explanation:

Let´s call O the place for the gas station, A the location point of police car ( at 5 miles east from the gas station ), and B the location point of the truck ( 12 miles south from a gas station.

The three points shape a right triangle with L (distance between police car and truck) then

L² = OA² + OB² at the point police car is 5 miles east and truck 12 miles south ( both from gas station)

L² = ( 5)² + (12)²

L = √ 25 + 144

L = √169

L = 13 miles

Pitagoras theorem establishes in a right triangle hypotenuse L is:

L² = a² + b² a and b are the legs then

In general

L² = x² + y ² x and y the legs over distance police-car/gas station and truck/gas station

Differentiation on both sides of the equation with respect to time give us:

2*L*DL/dt = 2*x*Dx/dt + 2*y*Dy/dt

Where Dx/dt = 130 m/h West Dy/dt = 100 m/h south

L = 13 m x = 5 m y = 12

Then by substitution

2*13*DL/dt = 2*5*130 + 2*12*100

DL/dt = (1300+ 2400) / 26

DL/dt = 142 m/h

DL/dt is positive then L s increasing

b) If truck speed is 70 m/h

DL/dt still positive but with smaller module, then L still increasing but at smaller speed

DL/dt = 1300 + 2*12*70

DL/dt = (1300 + 1680)/ 26

DL/dt = 114,6 m

7 0

3 years ago

Please help me!!! Will get brainliest!!!

Alex73 [517]

Using the formula
A = Pe^kt
Where A is the ending amount of population, P is the population k is a constant and 't' is time.

A = 0.39, t= 12 and p= 0.29
0.39= 0.29e^12k
1.34 = e^12k
ln1.34 = 12k
ln1.34/12 = k
K= 0.02

No the graph does not support his claim as k should be equal to 0.5

4 0

3 years ago

Write an equation in slope-intercept form for the line that is parallel to y = 4x - 5 and contains the point (6, "-10).

Jobisdone [24]

Answer:

The desired equation is y = 4x - 34

Step-by-step explanation:

Start with the general slope-intercept form y = mx + b.

The new line is parallel to y = 4x - 5, and so the slope of the new line is the same as that of the old one: 4. Then we have:

y = 4x + b

Find b. Do this by substituting 6 for x and -10 for y:

-10 = 4(6) + b. Then -10 - 24 = b, and b = -34.

The desired equation is y = 4x - 34

7 0

2 years ago