Exponentiële formules herleiden
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = 64 ⋅ 2^{-2 x - 3}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
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\(y = 64 ⋅ 2^{-2 x - 3}\)
\(\text{ } = 64 ⋅ 2^{-2 x} ⋅ 2^{-3}\)
\(\text{ } = 8 ⋅ 2^{-2 x}\)
1p
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\(y = 8 ⋅ (2^{-2})^{x}\)
\(\text{ } = 8 ⋅ (\frac{1}{4})^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {859 \over 12{,}8 ⋅ 2{,}67^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {859 \over 12{,}8 ⋅ 2{,}67^{x}} = {859 \over 12{,}8} ⋅ {1 \over 2{,}67^{x}} = {859 \over 12{,}8} ⋅ 2{,}67^{-x} = {859 \over 12{,}8} ⋅ (2{,}67^{-1})^{x}\)
1p
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\(y = {859 \over 12{,}8} ⋅ (2{,}67^{-1})^{x} = 67{,}109... ⋅ 0{,}3745...^{x} ≈ 67{,}1 ⋅ 0{,}375^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {683 ⋅ 1{,}49^{x} \over 63 ⋅ 0{,}75^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {683 ⋅ 1{,}49^{x} \over 63 ⋅ 0{,}75^{x}} = {683 \over 63} ⋅ {1{,}49^{x} \over 0{,}75^{x}} = {683 \over 63} ⋅ ({1{,}49 \over 0{,}75})^{x}\)
1p
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\(y = {683 \over 63} ⋅ ({1{,}49 \over 0{,}75})^{x} = 10{,}841... ⋅ 1{,}9866...^{x} ≈ 10{,}8 ⋅ 1{,}987^{x}\)
1p
Druk \(x\) uit in \(y \text{.}\)
3p
\(y = 18 + 3 ⋅ 9^{8 x - 2}\)
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\(y = 18 + 3 ⋅ 9^{8 x - 2}\)
\(3 ⋅ 9^{8 x - 2} = y - 18\)
\(9^{8 x - 2} = \frac{1}{3} y - 6\)
1p
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\(8 x - 2 = {}^{9}\!\log(\frac{1}{3} y - 6)\)
1p
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\(8 x = {}^{9}\!\log(\frac{1}{3} y - 6) + 2\)
\(x = \frac{1}{8} ⋅ {}^{9}\!\log(\frac{1}{3} y - 6) + \frac{1}{4}\)
1p