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nexus9112 [7]
3 years ago
10

A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35

* 3^x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture. A about 2.5 hours B about 4.5 hours C about 5.5 hours D about 3.5 hours
Mathematics
2 answers:
Zigmanuir [339]3 years ago
7 0
The answer is  <span>about 2.5 hours</span>
allochka39001 [22]3 years ago
6 0

Answer:

2.5

Step-by-step explanation:

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Solve for x if log 9 base x + log 3 base x^2 = 2.5​
Y_Kistochka [10]

Not sure if the equation is

\log_9x+\log_3(x^2)=\dfrac52

or

\log_x9+\log_{x^2}3=\dfrac52

  • If it's the first one:

9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot9^{\log_3(x^2)}

9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot(3^2)^{\log_3(x^2)}

9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{2\log_3(x^2)}

9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^2)^2}

9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^4)}

9^{\log_9x+\log_3(x^2)}=x\cdot x^4

9^{\log_9x+\log_3(x^2)}=x^5

On the other side of the equation, we'd get

9^{5/2}=(3^2)^{5/2}=3^{2\cdot(5/2)}=3^5

Then

x^5=3^5\implies\boxed{x=3}

  • If it's the second one instead, you can use the same strategy as above:

x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot x^{\log_{x^2}3}

x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot\left((x^2)^{1/2}\right)^{\log_{x^2}3}

(Note that this step assume x>0)

x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{(1/2)\log_{x^2}3}

x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{\log_{x^2}\sqrt3}

x^{\log_x9+\log_{x^2}3}=9\sqrt3

Then we get

9\sqrt3=x^{5/2}\implies x=(9\sqrt3)^{2/5}\implies\boxed{x=3}

6 0
3 years ago
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Answer:

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Step-by-step explanation:

its simple really.

7 0
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Answer:

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Step-by-step explanation:

(10 - 1)(10 - 2)(10 - 3)(10 - 10)

10-10 is zero and Anything multiply by a factor of 0 equal 0 so

0 is the answer

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svetoff [14.1K]

Answer:

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What is the probability that the next person you meet was not born in February? No leap years.​
Serjik [45]

Answer:

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3 years ago
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