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3 years ago

Describe a method for writing an exponential equation given a graph

Mathematics

1 answer:

Dominik [7]3 years ago

3 0

Explanation:

We can find the parameters of the exponential equation ...

y = a^(x-h) +k

1. Locate the horizontal asymptote. The y-value of that is the value of k.

2. Locate the point that is at y = k+1. The x-value of that is the value of h.

3. Locate the point that is at x = h+1. Subtract k from the y-value of that to find "a".

____

You have identified the three points on any exponential curve y = a^(x -h) +k. They are ...

(-∞, k) for growth, or (∞, k) for decay

(h, k+1)

(h+1, k+a) . . . . . for decay, (h -1, k+1/a) might be easier to find

_____

Comment on reflected curves

If the curve extends below the horizontal asymptote, it has been reflected about the x-axis. Reflect it across the x-axis, perform the above steps, then multiply the right side of the equation by -1.

_____

Additional note

If the value of h is not an integer, it might be easier to express the curve in the form ...

y = a·b^x +k

In this case, you can find the value of b by finding the y-values associated with three consecutive values of x. Call them (x, y1), (x+1, y2), (x+2, y3). Then ...

b = (y3 -y2)/(y2 -y1)

a = (y1 -k)/b^x . . . . . where x is the x-value of the first point, (x, y1)

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A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re

bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force $F$ and the distance $d$ that the object moves:

$W=Fd$

If $F$ is measured in newtons and $d$ in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

$W=\int\limits^b_a {f(x)} \, dx$

Hooke’s Law states that the force required to maintain a spring stretched $x$ units beyond its natural length is proportional to

$f(x)=kx$

where $k$ is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

$4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1$

Thus $F=x$

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

$W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18$

18 J is the work required to stretch a spring from 7 m to 13 m.

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2 years ago

Find the value of B in the following equation if you know it goes through the point (-5, -8):

MA_775_DIABLO [31]

86? I'm not sure, sorry.

I plugged in the x and y values of the point given

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3 years ago

Able, Ben and Cal each played a game able’s score was six times ben’s score, Cale score was a hird time of Able’s score write do

Feliz [49]

Answer:

6:1:2

Step-by-step explanation:

Let a = Able's score, b = Ben's score, and c = Cal's score.

Since

Able's score was 6 times Ben's score, that means a = 6b.

Cal's score was a third of Able's score, so that means c = a/3. And since a = 6b, that means c = 6b / 3 = 2b.

Thus, the ratio of Able's score to Ben's score to Cal's score, a:b:c, is 6:1:2, because c is twice as much as b and a is 6 times as much as b.

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3 years ago

-5+5/3x=2 solve for x

LenaWriter [7]

Answer: 21/5

Step-by-step explanation:

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3 years ago

The temperature of earth may be measured either by thermometers on the ground, which is an accurate but tedious method, or by se

qwelly [4]

Answer:

Analysis of variance (ANOVA) is the most accurate to estimate the difference

Step-by-step explanation:

Analysis of variance (ANOVA) is the best statistical method that can be used to determine the systematic difference between the mean values of two given set of population in any random experiment

In this case the two set of populations would be the one in which temperature is measured by thermometers on ground and sensor mounted in a space satellite.

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2 years ago