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3 years ago

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A temperature recorded in antarctica was -116 degrees fahrenheit. The teMPTURE rECORED iN tHE sHArA dESERT iS 131 dEGREES fAHREN

HEIT. HOW maNY dEGREES wARMER iS 131 dEGREES fAHRENHEIT tHAN -116 dEGREES fAhRENHEIT

1 answer:

Natalka [10]3 years ago

7 0

Step-by-step explanation:

Go from the negetive number to 0 to the positive number. -116 to 0 is 116. Then, 0 to 131 is 131. Do 116+131 then you will find your answer.

Hope this helps.

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A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

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A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

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C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

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where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

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$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

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$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

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B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

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