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vaieri [72.5K]
3 years ago
7

Decrease 140g by 25%

Mathematics
2 answers:
Ilia_Sergeevich [38]3 years ago
8 0

Answer:

• let's first get the percentage decrease:

= { \rm{100\% - 25 \% }} \\ { \rm{ = 75\%}}

• then multiply the percentage decrease with the mass given:

= { \tt{75\% \times 140}} \\  \\  = { \tt{ \frac{75}{100}  \times 140}} \\  \\  = { \underline{ \tt{ \:  \: 105 \: g \: }}}

Ivanshal [37]3 years ago
6 0

Answer:

let's first get the percentage decrease:

=100%−25%

=75%

• then multiply the percentage decrease with the mass given:

=75%×140

= 75/100 ×140

= 105g

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A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t
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Answer:

  • <u>Question 1:</u>      dm/dt=0.2m<u />

<u />

  • <u>Question 2:</u>     m=Ae^{(0.2t)}<u />

<u />

  • <u>Question 3:</u>      m=10e^{(0.2t)}<u />

<u />

  • <u>Question 4:</u>      m=10g<u />

Explanation:

<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>

<u></u>

a) By definition:  m'=dm/dt

b)  Given:  rate=0.2m

c) By substitution:  dm/dt=0.2m

<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>

a) <u>Separate variables</u>

     dm/m=0.2dt

b)<u> Integrate</u>

           \int dm/m=\int 0.2dt

            ln(m)=0.2t+C

c) <u>Antilogarithm</u>

       m=e^{0.2t+C}

       m=e^{0.2t}\cdot e^C

         e^C=A\\\\m=Ae^{(0.2t)}

<u>Question 3. Which particular solution matches the additional information?</u>

<u></u>

Use the measured rate of 4 grams per hour after 3 hours

            t=3hours,dm/dt=4g/h

First, find the mass at t = 3 hours

            dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g

Now substitute in the general solution of the differential equation, to find A:

          m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976

Round A to 1 significant figure:

  • A = 10.

<u>Particular solution:</u>

           

             m=10e^{(0.2t)}

<u>Question 4. What was the mass of the bacteria at time =0?</u>

Substitute t = 0 in the equation of the particular solution:

         m=10e^{0}\\\\m=10g

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Step-by-step explanation:

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