Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?
2 answers:
we have the function
we know that
In the equation of the exponential function of the form
a is the initial value
b is the base
x is the exponent
The initial value is the value of the function when the value of x is equal to zero
in this problem
for
the initial value is the point
therefore
the answer in the attached figure
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<h3>Answer:</h3>
<em>Try the answers</em>
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
_____
<em>Derive it</em>
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...