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3 years ago

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Explain what exponential decay is

2 answers:

Basile [38]3 years ago

5 0

A function in which the dependent variable decreases by the same factor over each unit of time

VARVARA [1.3K]3 years ago

5 0

A quantity X follows an exponential decay (decrease) if it decreases at a rate proportional to its current value. This can be written as

$X(t) = X_0 e^{-at}$

with t being the time (can be continuous or discrete steps), and "a" being a rate of decay (the larger "a" the faster the decay). X0 is an initial (at time 0) value of the quatity X. Exponential decay is seen frequently in nature (radioactivity, chemical reactions) and economics.

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The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm

mina [271]

Answer:

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

$V = \frac{4\pi r^3}{3}$

In this question:

We have to derivate V and r implicitly in function of time, so:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

The radius of a sphere is increasing at a rate of 3 mm/s.

This means that $\frac{dr}{dt} = 3$

How fast is the volume increasing when the diameter is 60 mm?

Radius is half the diameter, so $r = 30$ . We have to find $\frac{dV}{dt}$ . So

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3$

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

5 0

3 years ago

Three financial institutions, A,B,C, are offering different rates on a loan. Is a offer 3.15 % annual compounded monthly, B offe

coldgirl [10]

Answer:

Step-by-step explanation:

Given that interest rates are as follows:

Let P be 100 dollars for each.

A) 3.15% compounded monthly.

Hence amount = $100(1+\frac{3.15}{1200} )^{12}$

Final amount = 103.20 dollars

B) 2.25% compounded quarterly

Final amt. = $100(1+\frac{2.25}{400} )^4$

=102.27

C) 2.05% compounded daily

Amount = $100(1+\frac{2.05}{36500} )^{365}$

=102.07

Obviously A is the best deal.

8 0

3 years ago

Find two different planes whose intersection is theline:x = 6 + 3ty = -8 - 3tz = -1 - tWrite equations for each plane in the for

alina1380 [7]

Answer:

$x+y=-2$ and $3z-y=5$ are two such planes.

Step-by-step explanation:

To find the two planes whose intersection is the line

$x=6+3t\\ y=-8-3t\\ z=-1-t$

You can say that <em>t</em> is equal to this expression

$t=\frac{x-6}{3} =\frac{y+8}{-3}=-z-1$

Next,

$\frac{x-6}{3} =\frac{y+8}{-3}\\ \frac{y+8}{-3}=-z-1$

Then,

$x+y=-2$ and $3z-y=5$ are two such planes.

You can see in the image attached that the intersection of this planes is the line

$x=6+3t\\ y=-8-3t\\ z=-1-t$

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Answer:

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