Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = \frac{3}{64} ⋅ 4^{1\frac{1}{2} x + 3}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
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\(y = \frac{3}{64} ⋅ 4^{1\frac{1}{2} x + 3}\)
\(\text{ } = \frac{3}{64} ⋅ 4^{1\frac{1}{2} x} ⋅ 4^{3}\)
\(\text{ } = 3 ⋅ 4^{1\frac{1}{2} x}\)
1p
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\(y = 3 ⋅ (4^{1\frac{1}{2}})^{x}\)
\(\text{ } = 3 ⋅ 8^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {775 \over 4{,}4 ⋅ 2{,}35^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {775 \over 4{,}4 ⋅ 2{,}35^{x}} = {775 \over 4{,}4} ⋅ {1 \over 2{,}35^{x}} = {775 \over 4{,}4} ⋅ 2{,}35^{-x} = {775 \over 4{,}4} ⋅ (2{,}35^{-1})^{x}\)
1p
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\(y = {775 \over 4{,}4} ⋅ (2{,}35^{-1})^{x} = 176{,}136... ⋅ 0{,}4255...^{x} ≈ 176{,}1 ⋅ 0{,}426^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {361 ⋅ 1{,}05^{x} \over 73 ⋅ 1{,}24^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {361 ⋅ 1{,}05^{x} \over 73 ⋅ 1{,}24^{x}} = {361 \over 73} ⋅ {1{,}05^{x} \over 1{,}24^{x}} = {361 \over 73} ⋅ ({1{,}05 \over 1{,}24})^{x}\)
1p
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\(y = {361 \over 73} ⋅ ({1{,}05 \over 1{,}24})^{x} = 4{,}945... ⋅ 0{,}8467...^{x} ≈ 4{,}9 ⋅ 0{,}847^{x}\)
1p
Druk \(x\) uit in \(y \text{.}\)
3p
\(y = 6 + 3 ⋅ 9^{8 x + 7}\)
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\(y = 6 + 3 ⋅ 9^{8 x + 7}\)
\(3 ⋅ 9^{8 x + 7} = y - 6\)
\(9^{8 x + 7} = \frac{1}{3} y - 2\)
1p
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\(8 x + 7 = {}^{9}\!\log(\frac{1}{3} y - 2)\)
1p
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\(8 x = {}^{9}\!\log(\frac{1}{3} y - 2) - 7\)
\(x = \frac{1}{8} ⋅ {}^{9}\!\log(\frac{1}{3} y - 2) - \frac{7}{8}\)
1p