Question

The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5 2 28 Complete the chart and determine the solution of the equation f(x) = g(x).
x = −2

x = −1

x = 1

x = 20

Answer 1

Given equations are

f(x)=2x+24

$g(x)=5(0.5)^x$

Now we have to complete the table so that we can find for what value of x, both f(x) and g(x) are equal.

values in table are not clear so i will draw a fresh table using values x=-2,-1,0,1,2,3,4

I will show you calculation for x=-2

plug x=-2 into f(x) and g(x)

f(-2)=2(-2)+24=-4+24=20

$g(-2)=5(0.5)^{-2}=5(\frac{1}{2})^{-2}=5(\frac{1}{2^{-2}})=5(2^2)=5(4)=20$

Similarly you can find other values to complete the table.

From table we see that f(x) and g(x) both are equal to 20 when x=-2

Hence x=-2 is the final answer.