1/2 is the simpliest form,divide everything by 2
Ok so the triangle part is 10 but I don’t know what the rectangle part is but the formula for a rectangle is A=base x high
Let's take a look at the first few numbers in the sequence based on the given rule:
![a_{1}=6\\ a_{2}= \frac{1}{4}(6)\\ a_3= \frac{1}{4}\big( \frac{1}{4}\big)6= \big(\frac{1}{4}\big)^2(6)\\ a_{4}= \frac{1}{4} \big(\frac{1}{4}\big)^26= \big(\frac{1}{4}\big)^3(6)](https://tex.z-dn.net/?f=a_%7B1%7D%3D6%5C%5C%20a_%7B2%7D%3D%20%5Cfrac%7B1%7D%7B4%7D%286%29%5C%5C%20a_3%3D%20%5Cfrac%7B1%7D%7B4%7D%5Cbig%28%20%5Cfrac%7B1%7D%7B4%7D%5Cbig%296%3D%20%5Cbig%28%5Cfrac%7B1%7D%7B4%7D%5Cbig%29%5E2%286%29%5C%5C%20a_%7B4%7D%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Cbig%28%5Cfrac%7B1%7D%7B4%7D%5Cbig%29%5E26%3D%20%5Cbig%28%5Cfrac%7B1%7D%7B4%7D%5Cbig%29%5E3%286%29)
Inspecting this pattern it seems like the power
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
is being raised to is always one less than the number of the sequence, so if we were on the nth number in the sequence, that part of the expression would be
![\big(\frac{1}{4} \big)^{n-1}](https://tex.z-dn.net/?f=%20%5Cbig%28%5Cfrac%7B1%7D%7B4%7D%20%5Cbig%29%5E%7Bn-1%7D)
. We also know that we'll be multiplying whatever we get from that by 6, so we can write the full explicit rule for our sequence as
![a_n=6\big( \frac{1}{4} \big)^{n-1}](https://tex.z-dn.net/?f=a_n%3D6%5Cbig%28%20%5Cfrac%7B1%7D%7B4%7D%20%5Cbig%29%5E%7Bn-1%7D)
Where
![a_n](https://tex.z-dn.net/?f=a_n)
is the nth number in our sequence.
Answer:
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Step-by-step explanation:
Average rate of change:
The average rate of a function f(x) in an interval [a,b] is given by:
![A = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
In this question:
![D(q) = -0.0003q^2 - 0.04q + 23.56](https://tex.z-dn.net/?f=D%28q%29%20%3D%20-0.0003q%5E2%20-%200.04q%20%2B%2023.56)
What is the average rate of change of Demand between 40 and 175 units sold?
. So
![D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48](https://tex.z-dn.net/?f=D%2840%29%20%3D%20-0.0003%2A40%5E2%20-%200.04%2A40%20%2B%2023.56%20%3D%2021.48)
![D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725](https://tex.z-dn.net/?f=D%28175%29%20%3D%20-0.0003%2A175%5E2%20-%200.04%2A175%20%2B%2023.56%20%3D%207.3725)
So
![A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D%20%3D%20%5Cfrac%7B7.3725%20-%2021.48%7D%7B175%20-%2040%7D%20%3D%20-0.1045)
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.