Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = -\frac{8}{27} ⋅ 3^{x + 3}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
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\(y = -\frac{8}{27} ⋅ 3^{x + 3}\)
\(\text{ } = -\frac{8}{27} ⋅ 3^{x} ⋅ 3^{3}\)
\(\text{ } = -8 ⋅ 3^{x}\)
1p
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\(y = -8 ⋅ (3^{1})^{x}\)
\(\text{ } = -8 ⋅ 3^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {875 \over 16{,}7 ⋅ 2{,}58^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {875 \over 16{,}7 ⋅ 2{,}58^{x}} = {875 \over 16{,}7} ⋅ {1 \over 2{,}58^{x}} = {875 \over 16{,}7} ⋅ 2{,}58^{-x} = {875 \over 16{,}7} ⋅ (2{,}58^{-1})^{x}\)
1p
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\(y = {875 \over 16{,}7} ⋅ (2{,}58^{-1})^{x} = 52{,}395... ⋅ 0{,}3875...^{x} ≈ 52{,}4 ⋅ 0{,}388^{x}\)
1p
Herleid tot de gevraagde vorm.
2p
Schrijf de formule \(y = {546 ⋅ 0{,}54^{x} \over 19 ⋅ 1{,}07^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Rond \(b\) af op één decimaal en \(g\) op 3 decimalen.
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\(y = {546 ⋅ 0{,}54^{x} \over 19 ⋅ 1{,}07^{x}} = {546 \over 19} ⋅ {0{,}54^{x} \over 1{,}07^{x}} = {546 \over 19} ⋅ ({0{,}54 \over 1{,}07})^{x}\)
1p
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\(y = {546 \over 19} ⋅ ({0{,}54 \over 1{,}07})^{x} = 28{,}736... ⋅ 0{,}5046...^{x} ≈ 28{,}7 ⋅ 0{,}505^{x}\)
1p
Druk \(x\) uit in \(y \text{.}\)
3p
\(y = 27 + 3 ⋅ 2^{4 x + 7}\)
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\(y = 27 + 3 ⋅ 2^{4 x + 7}\)
\(3 ⋅ 2^{4 x + 7} = y - 27\)
\(2^{4 x + 7} = \frac{1}{3} y - 9\)
1p
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\(4 x + 7 = {}^{2}\!\log(\frac{1}{3} y - 9)\)
1p
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\(4 x = {}^{2}\!\log(\frac{1}{3} y - 9) - 7\)
\(x = \frac{1}{4} ⋅ {}^{2}\!\log(\frac{1}{3} y - 9) - 1\frac{3}{4}\)
1p