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Sagot :
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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