Question

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

x f(x) = 2.5x − 10.5 g(x) = 64(0.5^x)
2
3
4
5
6

Answer 1

If you would like to solve the equation 2.5 * x - 10.5 = 64 * 0.5 * x, you can calculate this using the following steps:

2.5 * x - 10.5 = 64 * 0.5 * x
2.5 * x - 10.5 = 32 * x
- 10.5 = 32 * x - 2.5 * x
- 10.5 = 29.5 * x
x = - 10.5 / 29.5
x = - 0.3559 = - 0.36

Answer 2

The values of a function are the true values of the function.

The value of x is 5

The functions are given as:

$\mathbf{f(x) = 2.5x - 10.5}$

$\mathbf{g(x) = 64(0.5^x)}$

When x = 2 to 6, we have:

$\mathbf{f(2) = 2.5(2) - 10.5 = -5.5}$

$\mathbf{f(3) = 2.5(3) - 10.5 = -3}$

$\mathbf{f(4) = 2.5(4) - 10.5 = -0.5}$

$\mathbf{f(5) = 2.5(5) - 10.5 = 2}$

$\mathbf{f(6) = 2.5(6) - 10.5 = 4.5}$

When x = 2 to 6, we have:

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

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

$\mathbf{g(4) = 64(0.5^4) =4}$

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

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

By comparison:

$\mathbf{f(5) = g(5) = 2}$

So, we have:

$\mathbf{x = 5}$

Hence, the value of x is 5

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