Mathematics, 15.01.2020 06:31 red21120p718de

Determining exponential growth and decay in exercise, use the given information to write an exponential equation for y. does the function represent exponential growth or exponential decay?
dy/dt = -2/3y, y = 20 when t = 0

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Answer from: queenkimm26

$y=20e^{-\frac{2}{3}t}$

Exponential decay

Step-by-step explanation:

We are given that

$\frac{dy}{dt}=-\frac{2}{3}y$

y=20 when t=0

$\frac{dy}{y}=-\frac{2}{3}dt$

Taking integration on both sides then we get

$lny=-\frac{2}{3}t+C$

Using formula $\int \frac{dx}{x}=lnx,\int dx=x$

$y=e^{-\frac{2}{3}t+C}$

Using formula

$lnx=y\implies x=e^y$

$y=e^C\cdot e^{-\frac{2}{3}t}$

e^C=Constant=C

$y=Ce^{-\frac{2}{3}t}$

Substitute y=20 and t=0

20=C

Substitute the value of C

$y=20e^{-\frac{2}{3}t}$

When t tends to infinity then

$\lim_{t\rightarrow\infty}=\lim_{t\rightarrow\infty}20e^{-\frac{2}{3}t}=0$

When time increases then the value of function decrease

Hence, the function is exponential decay.

Answer from: Quest

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be). so point b is at (-2,2). point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

Answer from: Quest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

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Determining exponential growth and decay in exercise, use the given information to write an exponent...

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