Answer:
See Explanation
Step-by-step explanation:
Incomplete question as the function is not given. So, I will give a general solution
Required
Determine the average rate of change from t = 2 to 4
Average rate of change is :
![Rate = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
In this case: a = 2 and b = 4
So, we have:
![Rate = \frac{f(4) - f(2)}{4 - 2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%284%29%20-%20f%282%29%7D%7B4%20-%202%7D)
![Rate = \frac{f(4) - f(2)}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%284%29%20-%20f%282%29%7D%7B2%7D)
Assume that the exponential function is:
![f(t) = 3^{-t](https://tex.z-dn.net/?f=f%28t%29%20%3D%203%5E%7B-t)
f(4) and f(2) will be:
![\\ f(4) = 3^{-4} = \frac{1}{81}](https://tex.z-dn.net/?f=%5C%5C%20f%284%29%20%3D%203%5E%7B-4%7D%20%3D%20%5Cfrac%7B1%7D%7B81%7D)
![f(2) = 3^{-2} = \frac{1}{9}](https://tex.z-dn.net/?f=f%282%29%20%3D%203%5E%7B-2%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D)
So:
![Rate = \frac{f(4) - f(2)}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7Bf%284%29%20-%20f%282%29%7D%7B2%7D)
![Rate = \frac{\frac{1}{81} - \frac{1}{9}}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B81%7D%20-%20%5Cfrac%7B1%7D%7B9%7D%7D%7B2%7D)
Take LCM
![Rate = \frac{\frac{1 - 9}{81}}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B%5Cfrac%7B1%20-%209%7D%7B81%7D%7D%7B2%7D)
![Rate = \frac{-\frac{8}{81}}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20%5Cfrac%7B-%5Cfrac%7B8%7D%7B81%7D%7D%7B2%7D)
![Rate = -\frac{8}{81}*\frac{1}{2}](https://tex.z-dn.net/?f=Rate%20%3D%20-%5Cfrac%7B8%7D%7B81%7D%2A%5Cfrac%7B1%7D%7B2%7D)
![Rate = -\frac{4}{81}](https://tex.z-dn.net/?f=Rate%20%3D%20-%5Cfrac%7B4%7D%7B81%7D)
<em>So, the average rate of change is a decrease of 4/81</em>
Answer:
Step-by-step explanation:
the coordinate of D is (3,-3) because it is 3 units right from the x axis and -3 units down in y axis.
Answer:
Gianna makes $18 per hour.
Step-by-step explanation:
Given Gianna makes 90$ for 5 hours. That means she should make
$ = 18$ every hour.
Therefore we have:
a.
HOURS DOLLARS
1 18
2 36
3 54
4 72
5 90
6 108
7 126
b.
For the tabular column mark Hours on the x - axis and Dollars on the Y - axis. It can be plotted from the above table easily.
c.
If Gianna works for 8 hours she would have made 8 X 18 = 144$.
So, she will earn 144$ in 8 hours.
d.
To make 60$ she would have to work
hours = 3.33 hours.
Answer: 12k+2
Step-by-step explanation:
A=7.51
B=3.49
C=1.371
D0.1371