taiwan-gsat 2023 Q10

taiwan-gsat · Other · gsat__math-b 5 marks Exponential Functions Applied/Contextual Exponential Modeling
An organization introduced two different nutrients into culture dishes A and B at 12 o'clock. At this time, the bacterial counts in dishes A and B are $X$ and $Y$ respectively. The quantity in dish A doubles every 3 hours; for example, at 3 PM the quantity in A is $2X$. The quantity in dish B doubles every 2 hours; for example, at 2 PM the quantity in B is $2Y$, and at 4 PM the quantity in B is $4Y$. Part of the measurement results are recorded in the table below. At 6 PM, the organization measured that the quantities in dishes A and B are the same. To estimate the bacterial quantities in dishes A and B from 12 o'clock to 12 midnight using an exponential growth model, select the correct options.
Time (o'clock)12131415161718192021222324
Quantity in A$X$$2X$
Quantity in B$Y$$2Y$$4Y$

(1) $X > Y$ (2) At 1 PM, the quantity in A is $\frac{4}{3}X$ (3) At 3 PM, the quantity in B is $3Y$ (4) At 7 PM, the quantity in B is 1.5 times that of A (5) At 12 midnight, the quantity in B is 2 times that of A
An organization introduced two different nutrients into culture dishes A and B at 12 o'clock. At this time, the bacterial counts in dishes A and B are $X$ and $Y$ respectively. The quantity in dish A doubles every 3 hours; for example, at 3 PM the quantity in A is $2X$. The quantity in dish B doubles every 2 hours; for example, at 2 PM the quantity in B is $2Y$, and at 4 PM the quantity in B is $4Y$. Part of the measurement results are recorded in the table below. At 6 PM, the organization measured that the quantities in dishes A and B are the same. To estimate the bacterial quantities in dishes A and B from 12 o'clock to 12 midnight using an exponential growth model, select the correct options.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Time (o'clock) & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\
\hline
Quantity in A & $X$ &  &  & $2X$ &  &  &  &  &  &  &  &  &  \\
\hline
Quantity in B & $Y$ &  & $2Y$ &  & $4Y$ &  &  &  &  &  &  &  &  \\
\hline
\end{tabular}
\end{center}

(1) $X > Y$
(2) At 1 PM, the quantity in A is $\frac{4}{3}X$
(3) At 3 PM, the quantity in B is $3Y$
(4) At 7 PM, the quantity in B is 1.5 times that of A
(5) At 12 midnight, the quantity in B is 2 times that of A