Question

1. Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).1. Be careful when putting exponents into your calculator- do then first and then the rest of the equation!
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2 16
3
4
5
6

Answer 1

Answer:

The solution is x=5

Step-by-step explanation:

We want to solve the equation;

$2.5x-10.5=64(0.5^x)$ by numerically plugging in some values of x into the corresponding functions.

We complete the table functions as shown below:

$\begin{center}\begin{tabular}{ c c c }x & f(x)=2.5x-10.5 &g(x)=64(0.5^x)\\ 2 & -5.5 & 16 \\ 3 & -3 & 8 \\ 4 & -0.5& 4 \\5 & 2 & 2\\6&4.5&1\\\end{tabular}\end{center}$

The solution to $2.5x-10.5=64(0.5^x)$ is the x-value of the point of intersection of the functions $f(x)=2.5x-10.5$ and $g(x)=64(0.5^x)$.

At this point the values of these two functions are equal.

From the table, the two functions are equal at (2,5)

Therefore x=5 is the required solution