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jonny [76]
2 years ago
5

20 points! Write an exponential function in the form y=ab^x that goes through points (0, 8) and (2, 200)

Mathematics
2 answers:
attashe74 [19]2 years ago
8 0

Answer:

y = 8(5) {}^{x}

Step-by-step explanation:

The normal exponential function is in form

y = ab {}^{x}

let plug in 0,8

8 = ab {}^{0}

b^0=1

so

8 = a \times 1 =  \:  \:  \:  \: a = 8

So so far our equation is

y = 8b {}^{x}

So now let plug in 2,200

200 = 8b {}^{2}

Divide 8 by both sides and we get

25 = b {}^{2}

\sqrt{25}

Which equal 5 so b equal 5. So our equation is

y = 8(5) {}^{x}

alexandr402 [8]2 years ago
4 0

Answer:

y=8(5)^x

Step-by-step explanation:

We want an exponential function that goes through the two points (0, 8) and (2, 200).

Since a point is (0, 8), this means that y = 8 when x = 0. Therefore:

8=a(b)^0

Simplify:

a=8

So we now have:

y = 8( b )^x

Likewise, the point (2, 200) tells us that y = 200 when x = 2. Therefore:

200=8(b)^2

Solve for b. Dividing both sides by 8 yields:

b^2=25

Thus:

b=5

Hence, our exponential function is:

y=8(5)^x

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The absurd came from assuming that A ∩ C ⊄ B ∪ D.

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2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

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The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

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