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 \(y = {702 \over 9{,}9 ⋅ 1{,}15^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (2) 00k8 - Exponentiële formules herleiden - basis - 0ms - dynamic variables a \(y = {702 \over 9{,}9 ⋅ 1{,}15^{x}} = {702 \over 9{,}9} ⋅ {1 \over 1{,}15^{x}} = {702 \over 9{,}9} ⋅ 1{,}15^{-x} = {702 \over 9{,}9} ⋅ (1{,}15^{-1})^{x}\) 1p ○ \(y = {702 \over 9{,}9} ⋅ (1{,}15^{-1})^{x} = 70{,}909... ⋅ 0{,}8695...^{x} ≈ 70{,}9 ⋅ 0{,}870^{x}\) 1p 2p b Schrijf de formule \(y = {283 ⋅ 0{,}65^{x} \over 16 ⋅ 1{,}12^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (3) 00k9 - Exponentiële formules herleiden - basis - 0ms - dynamic variables b \(y = {283 ⋅ 0{,}65^{x} \over 16 ⋅ 1{,}12^{x}} = {283 \over 16} ⋅ {0{,}65^{x} \over 1{,}12^{x}} = {283 \over 16} ⋅ ({0{,}65 \over 1{,}12})^{x}\) 1p ○ \(y = {283 \over 16} ⋅ ({0{,}65 \over 1{,}12})^{x} = 17{,}687... ⋅ 0{,}5803...^{x} ≈ 17{,}7 ⋅ 0{,}580^{x}\) 1p |