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3 years ago

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Two separate bacteria populations grow each month and are represented by the functions f(x) = 3x and g(x) = 7x + 6. In what mont

h is the f(x) population greater than the g(x) population? Month 1 Month 2 Month 3 Month 4

2 answers:

mars1129 [50]3 years ago

7 0

Answer:

The answer is Never.

Step-by-step explanation:

In order to determine the month, we have to graph both functions and then we have to determine the intercept point $(x_o,y_o)$ of the functions. With this information, for any "x" value greater than $x_o$ , one of both function will be greater that the other.

I have attached an image that shows the graph of both functions, where:

Red line: $f(x)=3*x$

Blue line: $g(x)=7*x+6$

As we see in the image, the intercept happens in the negative range of "x". Also we can see that the population of g(x) is always greater than f(x) for $x>0$ .

Therefore, never the f(x) population will be greater than g(x) population.

Murljashka [212]3 years ago

6 0

One month = 13
2 months = 20

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And we can find this probability on this way:

$P(0.2$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

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b) $P(X\geq 23)=P(\frac{X-\mu}{\sigma}\geq \frac{23-\mu}{\sigma})=P(Z\geq \frac{23-29}{5})=P(Z\geq -1.2)$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

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And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

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$X \sim N(29,5)$

Where $\mu=29$ and $\sigma=5$ with the values on this case representing millions

We are interested on this probability :

$P(30$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

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And we can find this probability on this way:

$P(0.2$

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$P(0.2$

Part b

We are interested on this probability :

$P(X\geq 23)$

$P(X\geq 23)=P(\frac{X-\mu}{\sigma}\geq \frac{23-\mu}{\sigma})=P(Z\geq \frac{23-29}{5})=P(Z\geq -1.2)$

And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.

$P(Z\geq -1.2)=1-P(Z$

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We are interested on this probability :

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And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.

$P(Z>2.2)=1-P(Z$

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