Match the cube roots and square roots with their values.
1 answer:
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Answer:
B) 25
Step-by-step explanation:
Given exponential function:
The growth factor between and
is 25.
To find the growth factor between and
Solution:
The growth factor of an exponential function in the interval and
is given by :
We can check this by plugging in the given points.
The growth factor between and
would be calculated as:
Plugging in values.
(On canceling the common terms)
(Using quotient property of exponents
)
∴
Similarly the growth factor between and
would be:
Plugging in values.
(On canceling the common terms)
(Using quotient property of exponents
)
∴
Thus, the growth factor remains the same which is =25.
Check the picture below.
Answer:
Part A)
The <em>x-</em>intercepts are (-1/4, 0) and (4, 0).
Part B)
The vertex is a maximum because the leading coefficient is negative.
The vertex is (1.875, 72.25).
Part C)
We can plot the zeros and the vertex, and connect them with a curve.
Step-by-step explanation:
The function given is:
Part A)
To find the <em>x-</em>intercepts of the function, set the function equal to 0 and solve for <em>x: </em>
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We can divide both sides by negative four:
Factor:
Zero Product Property:
Solve for each case:
Hence, our zeros are:
Part B)
Note that the leading coefficient of our function is negative.
So, our function will be concave down.
Hence, our vertex will be the maximum.
The vertex is given by:
In this case, <em>a </em>= -16, <em>b</em> = 60, and <em>c</em> = 16.
Find the <em>x-</em>coordinate of the vertex:
Substitute this back into the function to find the <em>y-</em>coordinate:
Hence, our vertex is:
Part C)
Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.
The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the <em>y-</em>intercept.
