Whakaoti i te 2P=Pe^0.07T

$$2 P = P e ^ { 0.07 T }$$

Whakaoti mō P

$$\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&T=\frac{100\ln(2)}{7}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te Pe^{0.07T} mai i ngā taha e rua.

$$2P-Pe^{0.07T}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-Pe^{0.07T}+2P=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te P.

$$\left(-e^{0.07T}+2\right)P=0$$

He hanga arowhānui tō te whārite.

$$\left(2-e^{\frac{7T}{100}}\right)P=0$$

Whakawehe 0 ki te 2-e^{0.07T}.

$$P=0$$

Whakaoti mō T

$$\left\{\begin{matrix}\\T=\frac{100\ln(2)}{7}\text{, }&\text{unconditionally}\\T\in \mathrm{R}\text{, }&P=0\end{matrix}\right.$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$Pe^{0.07T}=2P$$

Whakawehea ngā taha e rua ki te P.

$$e^{0.07T}=2$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(e^{0.07T})=\log(2)$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$0.07T\log(e)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(e).

$$0.07T=\frac{\log(2)}{\log(e)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$0.07T=\log_{e}\left(2\right)$$

Whakawehea ngā taha e rua o te whārite ki te 0.07, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$T=\frac{\ln(2)}{0.07}$$