An exponential model can be described by the function

where: a is the initial population or the starting number, b is the base and x is the number of periods elapsed.
When the base of an exponential model is greater than 1 it is called a growth factor, but when it is less than 1 it is called a decay factor.
Given the exponential model

n is the final output of the exponential model, 20.5 is the starting number, 0.6394 is the base and t is the number of periods/time elapsed.
Here, the base is 0.6394 which is less than 1, hence a decay factor.
Therefore, <span>the
base, b, of the exponential model is 0.6394; It is a
decay factor.</span>
Answer:
A: 
B: 
Step-by-step explanation:
<u>A:</u>
Our expression is
. We need to find some common factors. Clearly, we can see that both terms share the x² part, so we can definitely take that out:


Let's see if 96 is divisible by 6:
96 ÷ 6 = 16; since there's no remainder / the remainder is 0, we know 96 is divisible by 6, so we can also factor out 6:


Thus, the answer to part A is
.
<u>B:</u>
Look at the
part of the above factored expression. Notice that it is a difference of squares (because
and 16 = 4²), so we can write this as:


Now take a look at the
part. Again, it's a difference of squares because
and 4 = 2², so rewrite that as:


Put it all together:

Thus, the answer to part B is
.
Answer:
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Step-by-step explanation:
Answer:
sin(x) = 
x = 16.26°
Step-by-step explanation:
First use Pythagorean theorem to find the length of the hypotenuse. Use
. Since we know a and b we can plug in to find c. When we plug in we get:
. When we solve this out we get 25 = c.
Now that we know the value of c, we also know sin(x) =
. Using this we see that sin(x) =
.
To get the exact degree value of x, take the inverse sin of
:
which gives us 16.26020° rounded to 16.26°
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