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

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XKelvinidn

Answer:

[tex]y=8(5)^x[/tex]

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:

[tex]8=a(b)^0[/tex]

Simplify:

[tex]a=8[/tex]

So we now have:

[tex]y = 8( b )^x[/tex]

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

[tex]200=8(b)^2[/tex]

Solve for b. Dividing both sides by 8 yields:

[tex]b^2=25[/tex]

Thus:

[tex]b=5[/tex]

Hence, our exponential function is:

[tex]y=8(5)^x[/tex]

Answer:

[tex]y = 8(5) {}^{x} [/tex]

Step-by-step explanation:

The normal exponential function is in form

[tex]y = ab {}^{x} [/tex]

let plug in 0,8

[tex]8 = ab {}^{0} [/tex]

b^0=1

so

[tex]8 = a \times 1 = \: \: \: \: a = 8[/tex]

So so far our equation is

[tex]y = 8b {}^{x} [/tex]

So now let plug in 2,200

[tex]200 = 8b {}^{2} [/tex]

Divide 8 by both sides and we get

[tex]25 = b {}^{2} [/tex]

[tex] \sqrt{25} [/tex]

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

[tex]y = 8(5) {}^{x} [/tex]

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