Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).

Asked by maham237 @ in Mathematics viewed by 491 People

1. Complete the table below to solve the equation 2.5x – 10.5 = 64(0.5x).
x f(x) = 2.5x – 10.5 g(x) = 64(0.5x)

2

3

4

5

6

Answered by maham237 @


Question:

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

Answer:

The completed table is attached below

Solution:

Given that,

f(x)=2.5x-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

Substitute the x = 3 in f(x)

f(3)=2.5(3)-10.5\\\\f(3)=7.5-10.5\\\\f(3)=-3

Substitute the x = 4 in f(x)

f(4)=2.5(4)-10.5\\\\f(4)=10-10.5\\\\f(4)=-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

Substitute the x = 6 in f(x)

f(6)=2.5(6)-10.5\\\\f(6)=15-10.5\\\\f(6)=4.5

Also given that,

g(x)=64(0.5)^{x}

Substitute the x = 2 in g(x)

g(2)=64(0.5)^{2}\\\\g(2)=64(0.25)\\\\g(2)=16

Substitute the x = 3 in g(x)

g(3)=64(0.5)^{3}\\\\g(3)=64(0.125)\\\\g(3)=8

Substitute the x = 4 in g(x)

g(4)=64(0.5)^{4}\\\\g(4)=64(0.0625)\\\\g(4)=4

Substitute the x = 5 in g(x)

g(5)=64(0.5)^{5}\\\\g(5)=64(0.3125)\\\\g(5)=2

Substitute the x = 6 in g(x)

g(6)=64(0.5)^{6}\\\\g(6)=64(0.015625)\\\\g(6)=1


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