Whakaoti i te 4x(1+48%)^t=19

$$4 x ( 1 + 48 \% ) ^ { t } = 19$$

Whakaoti mō x

$$x=\frac{19\times \left(\frac{25}{37}\right)^{t}}{4}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{48}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$4x\left(1+\frac{12}{25}\right)^{t}=19$$

Tāpirihia te 1 ki te \frac{12}{25}, ka \frac{37}{25}.

$$4x\times \left(\frac{37}{25}\right)^{t}=19$$

He hanga arowhānui tō te whārite.

$$4\times \left(\frac{37}{25}\right)^{t}x=19$$

Whakawehea ngā taha e rua ki te 4\times \left(\frac{37}{25}\right)^{t}.

$$\frac{4\times \left(\frac{37}{25}\right)^{t}x}{4\times \left(\frac{37}{25}\right)^{t}}=\frac{19}{4\times \left(\frac{37}{25}\right)^{t}}$$

Mā te whakawehe ki te 4\times \left(\frac{37}{25}\right)^{t} ka wetekia te whakareanga ki te 4\times \left(\frac{37}{25}\right)^{t}.

$$x=\frac{19}{4\times \left(\frac{37}{25}\right)^{t}}$$

Whakawehe 19 ki te 4\times \left(\frac{37}{25}\right)^{t}.

$$x=\frac{19\times \left(\frac{25}{37}\right)^{t}}{4}$$

Whakaoti mō t (complex solution)

$$t=\frac{-\ln(x)+\ln(\frac{19}{4})}{\ln(\frac{37}{25})}+\frac{2\pi n_{1}i}{\ln(\frac{37}{25})}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq 0$$

Whakaoti mō t

$$t=\frac{-\ln(x)+\ln(\frac{19}{4})}{\ln(\frac{37}{25})}$$

$$x>0$$