Solve the problem.
-Approximately one-fourth of all glass bottles distributed will be recycled each year. A beverage company distributes 370,000 bottles. The number still in use after t years is given by the function $\mathrm { N } ( \mathrm { t } ) = 370,000 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { t } }$. After how many years will 40,000 bottles still be in use? Round your answer to the nearest tenth.
A) $2.2 \mathrm { yr }$
B) $3.1 \mathrm { yr }$
C) $0.6 \mathrm { yr }$
D) $1.6 \mathrm { yr }$

Question

Quizplus · Accepted Answer

We need to find the value of t such that N(t) = 40,000. 
\begin{align*}
370,000 \left( \frac{1}{4} ight)^t &= 40,000 \
\left( \frac{1}{4} ight)^t &= \frac{4}{37} \
t &= \frac{\log \frac{4}{37}}{\log \frac{1}{4}} \
&\approx 1.6 	ext{ years (rounded to the nearest tenth)}.
\end{align*}
Therefore, the answer is (D).

Solve the Problem N(t)=370,000(14)t\mathrm { N } ( \mathrm { t } ) = 370,000 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { t } }N(t)=370,000(41​)t

Solve the Problem $\mathrm { N } ( \mathrm { t } ) = 370,000 \left( \frac { 1 } { 4 } \right) ^ { \mathrm { t } }$