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DIA [1.3K]
3 years ago
5

Convert 500 cubic feet to liters then to gallons

Mathematics
1 answer:
V125BC [204]3 years ago
5 0

Answer:

500 cubic feet equals 14158.4 liters or 3740.25 gallons.

Step-by-step explanation:

We are asked to convert 500 cubic feet to liters then to gallons.

We know that one cubic feet equals 28.3168 liters.

\text{500 cubic feet to liters}=\text{500 cubic feet}\times \frac{\text{28.3168 liters}}{\text{cubic feet}}

\text{500 cubic feet to liters}=500\times \text{28.3168 liters}

\text{500 cubic feet to liters}=\text{14158.4 liters}

We know one liter equals 0.264172 gallons.

\text{14158.4 liters to gallons}=\text{14158.4 liters}\times\frac{0.264172\text{ gallons}}{\text{liter}}

\text{14158.4 liters to gallons}=14158.4 \times 0.264172\text{ gallons}

\text{14158.4 liters to gallons}=3740.2528448\text{ gallons}

\text{14158.4 liters to gallons}\approx 3740.25\text{ gallons}

Therefore, 500 cubic feet equals 14158.4 liters or 3740.25 gallons.

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Vlada [557]

Answer:

a)  y=12000(2)^{\frac{t}{50}}

b)  Approx. 27,569 bacteria

c)  About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

y=Ab^{\frac{t}{n}}

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

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y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}

b)

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Remember, t is in minutes, so

1 hour = 60 minutes

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Substituting, we get:

y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

<u></u>

c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103

After about 103 minutes, there will be 50,000 bacteria

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