Answer:
The equation 2.5x -10.5 = 64(0.5^x) is true when x=5
Step-by-step explanation:
we need to solve the equation 2.5x -10.5 = 64(0.5^x)
We have to put the given values of x in the functions f(x) and g(x) and find their values
x f(x) = 2.5x -10.5 g(x) = 64(0.5^x)
2 2.5(2)-10.5 = -5.5 64(0.5^2) = 16
3 2.5(3) - 10.5 = -3 64(0.5^3) = 8
4 2.5(4) - 10.5 = -0.5 64(0.5^4) = 4
5 2.5(5) - 10.5 = 2 64(0.5^5) = 2
6 2.5(6) - 10.5 = 4.5 64(0.5^6) = 1
So, we need to solve the equation 2.5x -10.5 = 64(0.5^x)
This holds when x = 5 as shown in the table above.
