Whakaoti i te 19=7+17e^-0.034t

$$19 = 7 + 17 e ^ { - 0.034 t }$$

Whakaoti mō t

$$t=\frac{500\ln(17)-500\ln(12)}{17}\approx 10.244314537$$

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.

$$7+17e^{-0.034t}=19$$

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$17e^{-0.034t}+7=19$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$17e^{-0.034t}=12$$

Whakawehea ngā taha e rua ki te 17.

$$e^{-0.034t}=\frac{12}{17}$$

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

$$\log(e^{-0.034t})=\log(\frac{12}{17})$$

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

$$-0.034t\log(e)=\log(\frac{12}{17})$$

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

$$-0.034t=\frac{\log(\frac{12}{17})}{\log(e)}$$

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

$$-0.034t=\log_{e}\left(\frac{12}{17}\right)$$

Whakawehea ngā taha e rua o te whārite ki te -0.034, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$t=\frac{\ln(\frac{12}{17})}{-0.034}$$