Getal & Ruimte (12e editie) - havo wiskunde A
'Exponentiële formules herleiden'.
| havo wiskunde A | 9.1 Lineaire en exponentiële groei |
opgave 1Herleid tot de gevraagde vorm. 2p a Schrijf de formule \(y = {732 \over 14{,}7 ⋅ 1{,}67^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (2) 00k8 - Exponentiële formules herleiden - basis - 0ms - dynamic variables a \(y = {732 \over 14{,}7 ⋅ 1{,}67^{x}} = {732 \over 14{,}7} ⋅ {1 \over 1{,}67^{x}} = {732 \over 14{,}7} ⋅ 1{,}67^{-x} = {732 \over 14{,}7} ⋅ (1{,}67^{-1})^{x}\) 1p ○ \(y = {732 \over 14{,}7} ⋅ (1{,}67^{-1})^{x} = 49{,}795... ⋅ 0{,}5988...^{x} ≈ 49{,}8 ⋅ 0{,}599^{x}\) 1p 2p b Schrijf de formule \(y = {568 ⋅ 0{,}97^{x} \over 67 ⋅ 0{,}59^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (3) 00k9 - Exponentiële formules herleiden - basis - 0ms - dynamic variables b \(y = {568 ⋅ 0{,}97^{x} \over 67 ⋅ 0{,}59^{x}} = {568 \over 67} ⋅ {0{,}97^{x} \over 0{,}59^{x}} = {568 \over 67} ⋅ ({0{,}97 \over 0{,}59})^{x}\) 1p ○ \(y = {568 \over 67} ⋅ ({0{,}97 \over 0{,}59})^{x} = 8{,}477... ⋅ 1{,}6440...^{x} ≈ 8{,}5 ⋅ 1{,}644^{x}\) 1p |