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 \(y = {533 \over 12 ⋅ 2{,}74^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (2) 00k8 - Exponentiële formules herleiden - basis - 0ms - dynamic variables a \(y = {533 \over 12 ⋅ 2{,}74^{x}} = {533 \over 12} ⋅ {1 \over 2{,}74^{x}} = {533 \over 12} ⋅ 2{,}74^{-x} = {533 \over 12} ⋅ (2{,}74^{-1})^{x}\) 1p ○ \(y = {533 \over 12} ⋅ (2{,}74^{-1})^{x} = 44{,}416... ⋅ 0{,}3649...^{x} ≈ 44{,}4 ⋅ 0{,}365^{x}\) 1p 2p b Schrijf de formule \(y = {302 ⋅ 1{,}07^{x} \over 78 ⋅ 1{,}35^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (3) 00k9 - Exponentiële formules herleiden - basis - 0ms - dynamic variables b \(y = {302 ⋅ 1{,}07^{x} \over 78 ⋅ 1{,}35^{x}} = {302 \over 78} ⋅ {1{,}07^{x} \over 1{,}35^{x}} = {302 \over 78} ⋅ ({1{,}07 \over 1{,}35})^{x}\) 1p ○ \(y = {302 \over 78} ⋅ ({1{,}07 \over 1{,}35})^{x} = 3{,}871... ⋅ 0{,}7925...^{x} ≈ 3{,}9 ⋅ 0{,}793^{x}\) 1p |