Hope you understand this! :DPart a)
section A<span><span>f<span>avg</span></span>=<span><span>4(2<span>)2</span>−4(2<span>)1</span></span><span>2−1</span></span>=8</span>section B <span><span>f<span>avg</span></span>=<span><span>4(2<span>)4</span>−4(2<span>)3</span></span><span>4−3</span></span>=32</span>
Part b)
The rate of change is greater between x = 3 and x = 4 than between x = 2 and x =1 because an exponential function's rate of change is increasing, unlike a linear function which has a constant rate of change.
Answer:
28 times
Step-by-step explanation:
Just multiply 0.7 by 40
Answer:
y = 3x/2 + 23 1/2
Or
y = 3x/2 + 47/2
Step-by-step explanation:
Find the slope
y = 3/2x - 3/2
Equation of a line
y = mx + c
m = 3/2
using a point slope form equation
Substitute the point into the equation
( -9 , 10)
y - y1 = m( x - x1)
x1 = -9
y1 = 10
y - 10 = 3/2( x - (-9)
y - 10 = 3/2( x + 9)
Open the bracket
y - 10 = (3x + 27)/2
y = ( 3x + 27)/2 + 10
LCM = 2
y = ( 3x + 27 + 20)/2
y = ( 3x + 47)/2
Separate to get the value of slope and intercept
y = 3x/2 + 47/2
y = 3x/2 + 23 1/2
The equation of the line is
y = 3x/2 + 23 1/2
<h3>
Answer: x = 1/2</h3>
=========================================================
Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
---------------------
Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
