which properties are present in a table that represents an exponential function in the form y=b^x when b>1
1 answer:
Answer:
The function has the property of exponential growth function.
Step-by-step explanation:
The exponential function is given by , where b > 1.
Now, for x = 0, we get y = 1,
For x = 1, we get y = b
For, x = 2, we get y = b²
And so on.
Now, as b > 1, so, b² > b > 1 and the values of y are increasing as the value of x increases.
Therefore, the function has the property of exponential growth function.
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Answer:
Step-by-step explanation:
hg(x) means you multiply h(x) times g(x) and then we will set it equal to .
hg(x) = which simplifies to
. Now set that equal to
:
and get everything on the same side and factor:
. Factor by grouping:
and factor out what's common in each set of ( ):
which factors out to
. But
factors somoe to:
(x + 1)(x - 1)(x - 1) = 0 So the solutions for this are
x = -1, 1
Answer:
And if we solve for a we got
So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.
so if the time is 393.2 or lower a boy would earn a certificate of recognition from the fitness association
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".
Solution to the problem
Let X the random variable that represent the time for this event of a population, and for this case we know the distribution for X is given by:
Where and
NOTE: For this case the fastest 10% is on the lower tail of the distribution
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.
so if the time is 393.2 or lower a boy would earn a certificate of recognition from the fitness association