https://peda.net/id/afa6f4f4419 2020-01-28T08:30:33+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/a668ec5241a 2020-01-28T09:49:02+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D500%5Ccdot1%7B%2C%7D02%5Ex" alt="f\left(x\right)=500\cdot1{,}02^x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=g%5Cleft(x%5Cright)%3D500%2B12x" alt="g\left(x\right)=500+12x"/><br/> b)<br/> 12 euron palkkio on parempi vaihtoehto 18 vuoteen asti, sen jälkeen korko on tuottavampi vaihtoehto<br/> pääoma on kaksinkertaistunut 35 (korko) tai 42 (palkkio) vuoden jälkeen<br/> pääoma on nelinkertaistunut 70 (korko) tai 125 (palkkio) vuoden jälkeen 2020-01-28T09:49:02+02:00 https://peda.net/id/93fd93f241a 2020-01-28T09:41:21+02:00 a)<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D100%5Ccdot2%5Ex" alt="f\left(x\right)=100\cdot2^x"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D100%5Ccdot1%7B%2C%7D15%5Ex" alt="f\left(x\right)=100\cdot1{,}15^x"/></div> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D100%5Ccdot0%7B%2C%7D8%5Ex" alt="f\left(x\right)=100\cdot0{,}8^x"/></div> 2020-01-28T09:41:21+02:00 https://peda.net/id/64a4420441a 2020-01-28T09:40:02+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a_1%3D%5Cfrac%7B60%7D%7B2%7D%3D30" alt="a_1=\frac{60}{2}=30"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=a_n%3D15%5Ccdot2%5En" alt="a_n=15\cdot2^n"/></div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=480%3D15%5Ccdot2%5En" alt="480=15\cdot2^n"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=n%3D5" alt="n=5"/><!--filtered attribute: style="display: inline;"--></div> 2020-01-28T09:40:02+02:00 https://peda.net/id/ca82e4f041a 2020-01-28T09:35:43+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Ex%3D8" alt="2^x=8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5%5Ex%3D1" alt="5^x=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><!--filtered attribute: style="display: inline;"--><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%5Ex%3D%5Cfrac%7B1%7D%7B9%7D" alt="3^x=\frac{1}{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-2" alt="x=-2"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=7x%3D%5Csqrt%7B7%7D" alt="7x=\sqrt{7}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D" alt="x^{\frac{1}{2}}"/><br/> e)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=7%5Ccdot4%5E%7B5x%7D%3D28" alt="7\cdot4^{5x}=28"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><br/> f)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5%5E%7B2x-7%7D%3D125" alt="5^{2x-7}=125"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5" alt="x=5"/> 2020-01-28T09:35:43+02:00 https://peda.net/id/1097ae4041a 2020-01-28T09:30:31+02:00 a) 145<br/> b) 35<br/> c) 25 2020-01-28T09:30:31+02:00 https://peda.net/id/4787d90e419 2020-01-28T09:17:44+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D2%7B%2C%7D1%5Ccdot1%7B%2C%7D06%5Ex" alt="f\left(x\right)=2{,}1\cdot1{,}06^x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(0%5Cright)%3D2%7B%2C%7D1%5Ccdot1%7B%2C%7D06%5E0%3D2%7B%2C%7D1" alt="f\left(0\right)=2{,}1\cdot1{,}06^0=2{,}1"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(7%5Cright)%3D2%7B%2C%7D1%5Ccdot1%7B%2C%7D06%5E7%3D3%7B%2C%7D1756...%5Capprox3%7B%2C%7D2" alt="f\left(7\right)=2{,}1\cdot1{,}06^7=3{,}1756...\approx3{,}2"/></div> <div>massa kasvaa 6% vuorokaudessa</div> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D2%7B%2C%7D6%5Ccdot0%7B%2C%7D96%5Ex" alt="f\left(x\right)=2{,}6\cdot0{,}96^x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(0%5Cright)%3D2%7B%2C%7D6%5Ccdot0%7B%2C%7D96%5E0%3D2%7B%2C%7D6" alt="f\left(0\right)=2{,}6\cdot0{,}96^0=2{,}6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(7%5Cright)%3D2%7B%2C%7D6%5Ccdot0%7B%2C%7D96%5E7%3D1%7B%2C%7D9537...%5Capprox2%7B%2C%7D0g" alt="f\left(7\right)=2{,}6\cdot0{,}96^7=1{,}9537...\approx2{,}0g"/></div> <div>massa vähenee 4% vuorokaudessa</div> 2020-01-28T09:17:44+02:00 https://peda.net/id/24fe7dd6419 2020-01-28T09:02:27+02:00 a) B14<br/> b) A34<br/> c) C<br/> d) D24 2020-01-28T09:02:27+02:00 https://peda.net/id/75f37af8419 2020-01-28T08:57:34+02:00 a)<br/> kasvava, sillä kantaluku on suurempi kuin 1<br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Ex%3D8" alt="2^x=8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Ex%3D2%5E3" alt="2^x=2^3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3C8" alt="f\left(x\right)&lt;8"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(3%5Cright)%3D8" alt="f\left(3\right)=8"/></div> <div>funktio on kasvava, joten </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3C8%7B%2C%7D%5C%20kun%5C%20x%3C3" alt="f\left(x\right)&lt;8{,}\ kun\ x&lt;3"/></div> 2020-01-28T08:57:34+02:00 https://peda.net/id/f06bfcca419 2020-01-28T08:53:50+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=450%5Ccdot3%5E2%3D4050" alt="450\cdot3^2=4050"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D450%5Ccdot3%5Ex" alt="f\left(x\right)=450\cdot3^x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(1%7B%2C%7D5%5Cright)%3D450%5Ccdot3%5E%7B1%7B%2C%7D5%7D%3D2338%7B%2C%7D268...%5Capprox2338%5C%20" alt="f\left(1{,}5\right)=450\cdot3^{1{,}5}=2338{,}268...\approx2338\ "/> 2020-01-28T08:53:50+02:00 https://peda.net/id/aeaa0cb4419 2020-01-28T08:51:59+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D0%7B%2C%7D834%5Ex%5Ccdot%20m" alt="f\left(x\right)=0{,}834^x\cdot m"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(10%5Cright)%3D0%7B%2C%7D834%5E%7B10%7D%5Ccdot%20m%3D0%7B%2C%7D162802...%5Capprox0%7B%2C%7D163" alt="f\left(10\right)=0{,}834^{10}\cdot m=0{,}162802...\approx0{,}163"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1-0%7B%2C%7D1628...%5Capprox83%7B%2C%7D7%5C%25" alt="1-0{,}1628...\approx83{,}7\%"/> 2020-01-28T08:51:59+02:00 https://peda.net/id/53fe7bca419 2020-01-28T08:42:18+02:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(%5Cfrac%7B1%7D%7B4%7D%5Cright)%5Ex" alt="f\left(x\right)=\left(\frac{1}{4}\right)^x"/></div> <div> </div> <div>millä muuttujan arvolla funktio saa arvon 16? entä arvon -1?</div> <div>ratkaise<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%5Cle1" alt="f\left(x\right)\le1"/></div> <div> </div> <div>ratkaisu</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D16" alt="f\left(x\right)=16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Cfrac%7B1%7D%7B4%7D%5Cright)%5Ex%3D16" alt="\left(\frac{1}{4}\right)^x=16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(4%5E%7B-1%7D%5Cright)%5Ex%3D4%5E2" alt="\left(4^{-1}\right)^x=4^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-2" alt="x=-2"/></div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D-1" alt="f\left(x\right)=-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Cfrac%7B1%7D%7B4%7D%5Cright)%5Ex%3D-1" alt="\left(\frac{1}{4}\right)^x=-1"/></div> <div>yhtälöllä ei ole ratkaisua, sillä eksponenttifunktion arvojoukko on ]0,∞], eli funktio ei saa negatiivisia arvoja millään muuttujan arvolla x</div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%5Cle1" alt="f\left(x\right)\le1"/></div> <div>yhtäsuuruus on voimassa kun</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/>, koska nyt eksponenttifunktion kantaluku on </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1%7D%7B4%7D%3C1" alt="\frac{1}{4}&lt;1"/>, funktio on vähenevä, eli epäyhtälön ratkaisu on <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle0" alt="x\le0"/></div> <div> </div> <div> </div> 2020-01-28T08:42:18+02:00