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Lina20 [59]
3 years ago
13

For the following exercises, find a formula for an exponential function that passes through the two points given. (0,6) and (3,7

50)
Mathematics
1 answer:
kirill [66]3 years ago
5 0

\boxed{\boxed{f(x)=6(5)^x}}

<h2>Explanation:</h2>

An exponential function is given by the following form:

y=ab^x \\ \\ Where: \\ \\ a \ is \ a \ constant \ and \ b \ is \ the \ base

Here we know two points:

(0,6) \ and \ (3,750)

\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}

Finally, our exponential function is:

\boxed{\boxed{f(x)=6(5)^x}}

<h2>Learn more:</h2>

Behavior of functions: brainly.com/question/12891789

#LearnWithBrainly

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What equation represents a parabola with a focus of (0,4) and a directrix of y=2
scZoUnD [109]
We know that

Any point <span>(x,y)</span> on the parabola is equidistant from the focus and the directrix

Therefore,

focus (0,4) and directrix of y=2

<span>√[<span>(x−0)</span></span>²+(y−4)²]=y−(2)

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x²+y²-8y+16=y²-4y+4

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the answer is

y= (x²/4)+3


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2 years ago
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