6. The table shows the equations Ms. Valez discussed in math class today.
2 answers:
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Answer: y = (5832/25)*(5/18)^x
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Explanation:
Any general exponential function is of the form
y = a*b^x
Plug in (x,y) = (3,5) and we get
y = a*b^x
5 = a*b^3
If you plug in (x,y) = (2,18), then we'll get this other equation
18 = a*b^2
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So we have this system of equations
From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.
Overall, we end up with b = 5/18
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Use that value of b to find 'a'
18 = a*b^2
18 = a*(5/18)^2
18 = a*(25/324)
18*(324/25) = a
a = 5832/25
You could use the other equation as well to find 'a'
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Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x
To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.