Question

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

Answer 1

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)

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