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 \(y = {542 \over 18{,}5 ⋅ 1{,}13^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (2) 00k8 - Exponentiële formules herleiden - basis - 0ms - dynamic variables a \(y = {542 \over 18{,}5 ⋅ 1{,}13^{x}} = {542 \over 18{,}5} ⋅ {1 \over 1{,}13^{x}} = {542 \over 18{,}5} ⋅ 1{,}13^{-x} = {542 \over 18{,}5} ⋅ (1{,}13^{-1})^{x}\) 1p ○ \(y = {542 \over 18{,}5} ⋅ (1{,}13^{-1})^{x} = 29{,}297... ⋅ 0{,}8849...^{x} ≈ 29{,}3 ⋅ 0{,}885^{x}\) 1p 2p b Schrijf de formule \(y = {548 ⋅ 0{,}67^{x} \over 14 ⋅ 1{,}04^{x}}\) in de vorm \(y = b ⋅ g^{x} \text{.}\) Herleiden (3) 00k9 - Exponentiële formules herleiden - basis - 0ms - dynamic variables b \(y = {548 ⋅ 0{,}67^{x} \over 14 ⋅ 1{,}04^{x}} = {548 \over 14} ⋅ {0{,}67^{x} \over 1{,}04^{x}} = {548 \over 14} ⋅ ({0{,}67 \over 1{,}04})^{x}\) 1p ○ \(y = {548 \over 14} ⋅ ({0{,}67 \over 1{,}04})^{x} = 39{,}142... ⋅ 0{,}6442...^{x} ≈ 39{,}1 ⋅ 0{,}644^{x}\) 1p |