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Answer:
t=87.36643 ≈ 87.4 minutes
Step-by-step explanation:
y=a(.5)^{\frac{t}{h}}
y=a(.5)
h
t
y=6 \hspace{15px} a=340 \hspace{15px} h=15 \hspace{15px} t=?
y=6a=340h=15t=?
6=340(.5)^{\frac{t}{15}}
6=340(.5)
15
t
\frac{6}{340}=\frac{340(.5)^{\frac{t}{15}}}{340}
340
6
=
340
340(.5)
15
t
0.0176471=(.5)^{\frac{t}{15}}
0.0176471=(.5)
15
t
\log(0.0176471)=\log((.5)^{\frac{t}{15}})
log(0.0176471)=log((.5)
15
t
)
\log(0.0176471)=\frac{t}{15}\log(.5)
log(0.0176471)=
15
t
log(.5)
Power Rule.
15\log(0.0176471)=t\log(.5)
15log(0.0176471)=tlog(.5)
Multiply by 15.
\frac{15\log(0.0176471)}{\log(.5)}=\frac{t\log(.5)}{\log(.5)}
log(.5)
15log(0.0176471)
=
log(.5)
tlog(.5)
Divide by log(.5).
t=\frac{-26.299915}{-0.30103}
t=
−0.30103
−26.299915
t=87.36643\approx 87.4 \text{ minutes}
t=87.36643≈87.4 minutes