Exponentiële formules herleiden
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = -\frac{10}{27} ⋅ 3^{2 x + 3}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
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\(y = -\frac{10}{27} ⋅ 3^{2 x + 3}\)
\(\text{ } = -\frac{10}{27} ⋅ 3^{2 x} ⋅ 3^{3}\)
\(\text{ } = -10 ⋅ 3^{2 x}\)
1p
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\(y = -10 ⋅ (3^{2})^{x}\)
\(\text{ } = -10 ⋅ 9^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {687 \over 16{,}9 ⋅ 1{,}66^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {687 \over 16{,}9 ⋅ 1{,}66^{x}} = {687 \over 16{,}9} ⋅ {1 \over 1{,}66^{x}} = {687 \over 16{,}9} ⋅ 1{,}66^{-x} = {687 \over 16{,}9} ⋅ (1{,}66^{-1})^{x}\)
1p
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\(y = {687 \over 16{,}9} ⋅ (1{,}66^{-1})^{x} = 40{,}650... ⋅ 0{,}6024...^{x} ≈ 40{,}7 ⋅ 0{,}602^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {430 ⋅ 0{,}82^{x} \over 67 ⋅ 0{,}59^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {430 ⋅ 0{,}82^{x} \over 67 ⋅ 0{,}59^{x}} = {430 \over 67} ⋅ {0{,}82^{x} \over 0{,}59^{x}} = {430 \over 67} ⋅ ({0{,}82 \over 0{,}59})^{x}\)
1p
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\(y = {430 \over 67} ⋅ ({0{,}82 \over 0{,}59})^{x} = 6{,}417... ⋅ 1{,}3898...^{x} ≈ 6{,}4 ⋅ 1{,}390^{x}\)
1p
Druk \(x\) uit in \(y \text{.}\)
3p
\(y = 32 + 4 ⋅ 3^{9 x + 6}\)
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\(y = 32 + 4 ⋅ 3^{9 x + 6}\)
\(4 ⋅ 3^{9 x + 6} = y - 32\)
\(3^{9 x + 6} = \frac{1}{4} y - 8\)
1p
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\(9 x + 6 = {}^{3}\!\log(\frac{1}{4} y - 8)\)
1p
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\(9 x = {}^{3}\!\log(\frac{1}{4} y - 8) - 6\)
\(x = \frac{1}{9} ⋅ {}^{3}\!\log(\frac{1}{4} y - 8) - \frac{2}{3}\)
1p