Whakaoti i te 0.85=1{0.5}^frac{t{15.05}}

$$0.85 = 1 { 0.5 }^{ \frac{ t }{ 15.05 } }$$

Whakaoti mō t

$$t=\frac{301\log_{2}\left(\frac{5}{17}\right)}{20}+30.1\approx 3.528702067$$

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

Whakawehea ngā taha e rua ki te 1.

$$\frac{0.85}{1}=0.5^{\frac{t}{15.05}}$$

Whakarohaina te \frac{0.85}{1} mā te whakarea i te taurunga me te tauraro ki te 100.

$$\frac{85}{100}=0.5^{\frac{t}{15.05}}$$

Whakahekea te hautanga \frac{85}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{17}{20}=0.5^{\frac{t}{15.05}}$$

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

$$0.5^{\frac{t}{15.05}}=\frac{17}{20}$$

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

$$0.5^{\frac{20}{301}t}=0.85$$

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

$$\log(0.5^{\frac{20}{301}t})=\log(0.85)$$

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

$$\frac{20}{301}t\log(0.5)=\log(0.85)$$

Whakawehea ngā taha e rua ki te \log(0.5).

$$\frac{20}{301}t=\frac{\log(0.85)}{\log(0.5)}$$

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

$$\frac{20}{301}t=\log_{0.5}\left(0.85\right)$$

Whakawehea ngā taha e rua o te whārite ki te \frac{20}{301}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$t=-\frac{\frac{\ln(\frac{17}{20})}{\ln(2)}}{\frac{20}{301}}$$