<em><u>Question:</u></em>
complete the table below to solve the equation
f(x) = 2.5x – 10.5 g(x) = 64(0.5^x)
x = 2, 3, 4, 5, 6
<em><u>Answer:</u></em>
The completed table is attached below
<em><u>Solution:</u></em>
Given that,
![f(x)=2.5x-10.5](https://tex.z-dn.net/?f=f%28x%29%3D2.5x-10.5)
Substitute the x = 2 in f(x)
![f(2)=2.5(2)-10.5\\\\f(2)=5-10.5\\\\f(2)=-5.5](https://tex.z-dn.net/?f=f%282%29%3D2.5%282%29-10.5%5C%5C%5C%5Cf%282%29%3D5-10.5%5C%5C%5C%5Cf%282%29%3D-5.5)
Substitute the x = 3 in f(x)
![f(3)=2.5(3)-10.5\\\\f(3)=7.5-10.5\\\\f(3)=-3](https://tex.z-dn.net/?f=f%283%29%3D2.5%283%29-10.5%5C%5C%5C%5Cf%283%29%3D7.5-10.5%5C%5C%5C%5Cf%283%29%3D-3)
Substitute the x = 4 in f(x)
![f(4)=2.5(4)-10.5\\\\f(4)=10-10.5\\\\f(4)=-0.5](https://tex.z-dn.net/?f=f%284%29%3D2.5%284%29-10.5%5C%5C%5C%5Cf%284%29%3D10-10.5%5C%5C%5C%5Cf%284%29%3D-0.5)
Substitute the x = 5 in f(x)
![f(5)=2.5(5)-10.5\\\\f(5)=12.5-10.5\\\\f(5)=2](https://tex.z-dn.net/?f=f%285%29%3D2.5%285%29-10.5%5C%5C%5C%5Cf%285%29%3D12.5-10.5%5C%5C%5C%5Cf%285%29%3D2)
Substitute the x = 6 in f(x)
![f(6)=2.5(6)-10.5\\\\f(6)=15-10.5\\\\f(6)=4.5](https://tex.z-dn.net/?f=f%286%29%3D2.5%286%29-10.5%5C%5C%5C%5Cf%286%29%3D15-10.5%5C%5C%5C%5Cf%286%29%3D4.5)
Also given that,
![g(x)=64(0.5)^{x}](https://tex.z-dn.net/?f=g%28x%29%3D64%280.5%29%5E%7Bx%7D)
Substitute the x = 2 in g(x)
![g(2)=64(0.5)^{2}\\\\g(2)=64(0.25)\\\\g(2)=16](https://tex.z-dn.net/?f=g%282%29%3D64%280.5%29%5E%7B2%7D%5C%5C%5C%5Cg%282%29%3D64%280.25%29%5C%5C%5C%5Cg%282%29%3D16)
Substitute the x = 3 in g(x)
![g(3)=64(0.5)^{3}\\\\g(3)=64(0.125)\\\\g(3)=8](https://tex.z-dn.net/?f=g%283%29%3D64%280.5%29%5E%7B3%7D%5C%5C%5C%5Cg%283%29%3D64%280.125%29%5C%5C%5C%5Cg%283%29%3D8)
Substitute the x = 4 in g(x)
![g(4)=64(0.5)^{4}\\\\g(4)=64(0.0625)\\\\g(4)=4](https://tex.z-dn.net/?f=g%284%29%3D64%280.5%29%5E%7B4%7D%5C%5C%5C%5Cg%284%29%3D64%280.0625%29%5C%5C%5C%5Cg%284%29%3D4)
Substitute the x = 5 in g(x)
![g(5)=64(0.5)^{5}\\\\g(5)=64(0.3125)\\\\g(5)=2](https://tex.z-dn.net/?f=g%285%29%3D64%280.5%29%5E%7B5%7D%5C%5C%5C%5Cg%285%29%3D64%280.3125%29%5C%5C%5C%5Cg%285%29%3D2)
Substitute the x = 6 in g(x)
![g(6)=64(0.5)^{6}\\\\g(6)=64(0.015625)\\\\g(6)=1](https://tex.z-dn.net/?f=g%286%29%3D64%280.5%29%5E%7B6%7D%5C%5C%5C%5Cg%286%29%3D64%280.015625%29%5C%5C%5C%5Cg%286%29%3D1)
For the first one, it would be a mile every half hour, or a mile and a half every hour. The second one would be 1 mile every twenty minutes. I think it would be safe to say an 1 hour and a half or answer choice "D" for this problem.
Let me now if I can be more of an assistance!
Answer:
20 + 1 + 0.9 + 0.07
Step-by-step explanation:
Given the number 21.97 ;
To wite in expanded form:
Tens ___ Unit ____ tenth ____ hundredth
2_______ 1 _______ 9_________ 7
2 = 20
1 = 1
9 = 0.9
7 = 0.07
Hence,
20 + 1 + 0.9 + 0.07
The average rate of change in h(t) between t = 1 second and t = 3 is:
(h(3) - h(1))/(3 - 1) = ((3 + 70*3 - 16*3^2) - (3 + 70*1 - 16*1^2))/2 = 6
The average rate of change in h(t) between t=1 and t=3 tells us that that average speed between these points is 6 ft/s.