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Darya [45]
3 years ago
12

A 0.3 ml dose of a drug is injected into a patient steadily for 0.65 seconds. At the end of this time, the quantity, , of the dr

ug in the body starts to decay exponentially at a continuous rate of 0.35 percent per second. Using formulas, express as a continuous function of time, , in seconds.
Mathematics
1 answer:
Darya [45]3 years ago
4 0
Use the compound interest formula: A=P(1+i)^t.

P is the initial amount of the drug, 0.3ml.
i is - 0.0035.
t is in seconds.

You'll get:
A=0.3(1-0.0035)^t.

Sub in any value on t to find out how many ml are left t seconds after injection.

The 0.65 second injection time does not seem to be relevant as the question clearly states that the exponential decay starts AFTER the injection is completed.
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DIA [1.3K]

Answer:

y = \frac{3}{2} x + 13

Step-by-step explanation:

1) Use point-slope formula y-y_1 = m (x-x_1) to find the slope-intercept form (or y = mx + b form) of the equation. m represents the slope, and x_1 and y_1 represent the x and y values of a point the line intersects. So, substitute \frac{3}{2} for m, -4 for x_1, and 7 for y_1. Then, simplify and isolate y on the left side like so:

y-(7) = \frac{3}{2} (x - (-4)) \\y -7 = \frac{3}{2} (x + 4) \\y - 7 = \frac{3}{2} x + 6\\y = \frac{3}{2} x + 13

3 0
2 years ago
The length of the sides DEF are 12,16,and 20. Find the perimeter of the triangle formed by connection the midpoints of the sides
Mekhanik [1.2K]

Answer:

  • 24 units

Step-by-step explanation:

According to the midsegment theorem, the length of each side of the formed triangle is the half the parallel side of DEF.

<u>So the perimeter is:</u>

  • P = 1/2(12 + 16 + 20) = 24
6 0
1 year ago
Dr. Spike is a big fan of Bojangles and is particularly interested in the popularity of its celebrated wings dinner. Starting fr
Effectus [21]

Answer:

c

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6 0
3 years ago
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
amm1812

Answer:

a)   x₁ = 14

     x₂ = - 6

b) x = 4

c) P(max ) = 4000000 $

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x²  - 32x  - 336  = 0       or    x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8  ±√(64) + 336 ]/2

x₁,₂ = [ 8  ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁  = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32  ⇒  P´(x) = 0     - 8x + 32

x = 32/8

x = 4    Company has to sell  4 ( 4000 snowboard)

to get  a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64  + 128 + 336

P(max) = 400           or  400* 10000 =  4000000

     

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