We are given the function:
g(x) = 6 (4)^x
Part A.
To get the average rate of change, we use the formula:
average rate of change = [g(x2) – g(x1)] / (x2 – x1)
Section A:
average rate of change = [6 (4)^1 – 6 (4)^0] / (1 – 0) =
18
Section B:
average rate of change = [6 (4)^3 – 6 (4)^2] / (3 – 2) =
288
Part B.
288 / 18 = 16
Therefore the average rate of change of Section B is 16 times
greater than in Section A.
<span>The average rate of change is greater between x = 2 to x = 3 than between
x = 1 and x = 0 because an exponential function's rate of change increases
with increasing x (not constant).</span>
Answer:
∛27 = 3
Step-by-step explanation:
A radical is simply a fractional exponent: ![a^{(\frac{m}{n})} = \sqrt[n]{a^{m} }](https://tex.z-dn.net/?f=a%5E%7B%28%5Cfrac%7Bm%7D%7Bn%7D%29%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%20%7D)
Hence, ∛27 = 
Since 27 = 3³, then:
You could rewrite ∛27 as ∛(3)³.
![\sqrt[3]{3^{(3)} } = 3^{[(3)*(\frac{1}{3})]}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%5E%7B%283%29%7D%20%7D%20%3D%203%5E%7B%5B%283%29%2A%28%5Cfrac%7B1%7D%7B3%7D%29%5D%7D)
Multiplying the fractional exponents (3 × 1/3) will result in 1 (because 3 is the <u><em>multiplicative inverse</em></u> of 1/3). The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1.
Therefore, ∛27 = 3.
It takes about 15 minutes to cover 5/8²
Answer:
k=-1
Step-by-step explanation:
1-2k-2k=5
1-4k=5
4k=1-5
4k=-4
k=-4/4
k=-1