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KatRina [158]
3 years ago
5

Judy is a doctor. She placed a small sample of bacteria in a culture dish and recorded the number of bacteria present each 30 mi

nutes beginning at 12 PM. The table shows Judy's data. If the patten of bacterial growth remains constant, how many bacteria should be present in the culture dish at 2:00 PM?

Mathematics
1 answer:
german3 years ago
3 0

Answer:

At 2:00 there will be 38,400 bacteria.

Step-by-step explanation:

600/150 = 4

2400/600 = 4

So, the bacteria quadruples every half hour.

At 1:30, there will be 2400*4 = 9600.

At 2:00, there will be 9600*4= 38400

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Step-by-step explanation:

\large{\underline{\underline{\bf{\purple{Solution\:  : - }}}}}

\begin{gathered}\\  \dashrightarrow{\sf{3\dfrac{1}{5}} + 75\% - {1\dfrac{3}{10}}} \\  \end{gathered}

\red \divideontimes Firstly, converting mixed fractions into improper fraction.

\begin{gathered} \\  {\dashrightarrow{\sf{\dfrac{(3 \times 5) + 1}{5}} + 75\% - {\dfrac{(1 \times 10) + 3}{10}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\dfrac{15 + 1}{5}} + 75\% - {\dfrac{10 + 3}{10}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\dfrac{16}{5}} + 75\% - {\dfrac{13}{10}}}} \\ \end{gathered}

\red \divideontimes As we know that, 1% = 1/100, then converting 75% into improper fraction.

\begin{gathered}\\{\dashrightarrow{\sf{\dfrac{16}{5}} +  \dfrac{75}{100}  - {\dfrac{13}{10}}}} \\  \end{gathered}

\red \divideontimes According to the BODMAS, Firstly we will perform the addition.

\begin{gathered}\\{\dashrightarrow{\sf{\bigg(\dfrac{16}{5}} +  \dfrac{75}{100} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\red \divideontimes Taking the LCM of denominators.

\begin{gathered}\\{\dashrightarrow{\sf{\bigg(\dfrac{(16 \times 20) + (75 \times 1)}{100}} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\bigg(\dfrac{320 + 75 }{100}} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\bigg(\dfrac{395 }{100}} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\red \divideontimes Now, converting 395/100 in simplest form.

\begin{gathered}\\  {\dashrightarrow{\sf{\bigg( \cancel{\dfrac{395 }{100}}} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\bigg(\dfrac{79}{20}} \bigg)  - {\dfrac{13}{10}}}} \\ \end{gathered}

\red \divideontimes Now, performing subtraction, according to BODMAS.

\begin{gathered}\\  {\dashrightarrow{\sf{\dfrac{79}{20}}   - {\dfrac{13}{10}}}} \\ \end{gathered}

\red \divideontimes Again, taking LCM of denominators.

\begin{gathered}\\  {\dashrightarrow{\sf{\dfrac{(79 \times 1) - (13 \times 2)}{20}}}} \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\dfrac{79 -26}{20}}}}  \\ \end{gathered}

\begin{gathered}{\dashrightarrow{\sf{\dfrac{53}{20}}}} \\  \end{gathered}

\begin{gathered}\red{\bigstar{\underline{\boxed{\bf{Answer = \dfrac{53}{20}}}}}}\end{gathered}

<u>∴ The answer is 53/20.</u>

\begin{gathered}\end{gathered}

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