Solve the equation for a.
1 answer:
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Answer:
The graph in the attached figure
Step-by-step explanation:
we have
This is a exponential function of the form
where
a is the initial value or the y-intercept
b is the base of the exponential function
If b>1 then is a exponential growth function
If b<1 then is a exponential decay function
In this problem
The y-intercept is equal to
For x=0
The y-intercept is the point (0,1)
so
The value of b is greater than 1
so
Is a growth function
To plot the graph create a table with different values of x and y
For x=-1
f(x)=2^-1=0.5
point (-1,0.5)
For x=1
point (1,2)
For x=2
point (2,4)
For x=3
point (3,8)
For x=4
f(x)=2^4=16
point (4,16)
Plot the y-intercept and the other points and connect them to graph the exponential function
Note that as x increases the value of y increases (exponential growth function)
The graph in the attached figure
Domain of a function
<h2>STEP 3: finding the x values that make x²-6x-55>0 (factoring)</h2>
<h2>STEP 4: finding the x values that make (x+5)(x-11)>0 (factoring)</h2>
We want to find the domain of the following function:
This means that we want to find the x-values that it can take.
<h2>STEP 1: analyzing the simplies form of the function</h2>Let's analyze the simpliest form of the function:
Its graph is:
Then, for the simpliest form of the function, the x-values can only be higher than 0.
This means that its domain is
domain = x > 0
<h2>STEP 2: domain of the given function</h2>Based on the above we can deduce that for the <em>ln(x)</em> function, what is inside the parenthesis should be higher than 0 on this kind of functions.
This is that for
then
In order to find the values of x that make
we must factor it.
We want to find a pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6).
For the last term of the polynomial: -55, we have that
(-5) · 11 = 55
5 · (-11) = 11
If we add them:
-5 + 11 = 6
5 - 11 = -6
The pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6), are: 5 and -11
We use them to factor the polynomial:
Then,
In order to find them, we are going to separate the factors (x+5) and (x-11) and analyze when they are positive or negative:
Combining them:
Since we are going to multiply both factors:
We use the diagram to analyze the sign of their product:
Then
when x < -5 and when x > 11. This is the domain.
Therefore, expressed in set notation:
domain = {x|x∈(-∞, -5)∪(11, ∞)}
<h2>Answer: domain = {x | x ∈ (-∞, -5)∪(11, ∞)}</h2>