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e-lub [12.9K]
3 years ago
7

Find the equation of the exponential function represented by the table below:

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0

Given:

The table of values.

To find:

The equation of the exponential function represented by the table.

Solution:

The general form of an exponential function is

y=ab^x          ...(i)

where, a is initial value and b is growth factor.

From the given table it is clear that the function passes through (0,3) and (1,1.5). So, the must be satisfy by these points.

Putting x=0 and y=3 in (i), we get

3=ab^0

3=a(1)

3=a

Putting a=3, x=1 and y=1.5 in (i), we get

1.5=3b^1

\dfrac{1.5}{3}=b

\dfrac{1}{2}=b

Putting a=3 and b=\dfrac{1}{2} in (i), we get

y=3\left(\dfrac{1}{2}\right)^x

Therefore, the required equation for exponential function is y=3\left(\dfrac{1}{2}\right)^x.

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(-2)+(-2)+(-2)+(-2)
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3 years ago
2x-3y=2 for graphing systems of linear equations
Galina-37 [17]

Answer:

-2/3 is the y intercept

Step-by-step explanation:

So to find the y-intercept you must first put this in Slope-intercept form, I believe the form it is in right now is called standard form.

To get it into slope intercept form, we have to isolate y:

subtract 2x from both sides:

-3y = -2x + 2

Divide both sides by -3:

y = (2/3)x - 2/3

Now that we have slope-intercept form, we can find the y-intercept. We know slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case the y-intercept is -2/3.

Hope this helps!

7 0
3 years ago
Fill in the blanks to show the steps in solving the inequality -2x + 12<-4
professor190 [17]
-2x + 12 < - 4......subtract 12 from both sides
-2x + 12 - 12 < -4 - 12....simplify
-2x < -16...divide both sides by -2, changing the inequality sign
(-2/-2)x > -16/-2....simplify
x > 8
8 0
3 years ago
Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).
Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0
3 years ago
X=3 and y=4<br>whats the answer to this?<br><img src="https://tex.z-dn.net/?f=6%282x%20%2B%205y%29" id="TexFormula1" title="6(2x
IgorLugansk [536]
6(2x + 5y)
6[2(3) + 5(4)]
6[6 + 20]
6(26)
156

The answer is 156

Hope this helps :)
4 0
3 years ago
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