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Mandarinka [93]
1 year ago
12

On a piece of paper, graph f(x) = 4 x (0.5)^x

Mathematics
1 answer:
tangare [24]1 year ago
6 0

The complete question is

"On a piece of paper, graph f(x) = 4. (0.5)^x Then determine which answer choice matches the graph you drew."

The given function is an exponential function. The graph of option C is the correct answer.

<h3>What are exponential functions?</h3>

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

For example, y^x

, where a is a constant is an exponential function.

The function is given as

f(x) = 4. (0.5)^x

AS we can see that the given function is an exponential function.

Thus, the graph of option C is the correct answer.

Learn more about exponential here:

brainly.com/question/2193820

#SPJ1

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If dy/dx = x(y-1), find the equation of the tangent line at x=-2 with f(-2)=3
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Answer:

The equation of the tangent line passing through the point (-2,3) is

 4 x + y +5 =0

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the slope of the tangent</em>

<em>              </em>m = \frac{dy}{dx} = x(y-1)<em></em>

<em>              m = -2( 3-1) = -4</em>

<em>Given point x = -2</em>

<em>          y = f(-2) =3</em>

<em>∴The given point ( x₁ , y₁) = ( -2 ,3)</em>

<u><em>Step(ii):-</em></u>

The equation of the tangent line passing through the point (-2,3)

y - y_{1} = m(x-x_{1} )

y -3 = -4(x-(-2))

y -3 = -4( x+2)

y-3 = -4x -8

4x + y -3+8=0

4x +y +5=0

<u><em>Step(iii):-</em></u>

<em>The equation of the tangent line passing through the point (-2,3) is</em>

<em>   4 x + y +5 =0</em>

<em></em>

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2 years ago
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