Final answer:
To find the x intercepts of the equation y = x(0.4 - 0.008x), set y = 0 and solve for x using factoring or the quadratic formula.
Step-by-step explanation:
To find the x intercepts of the equation y = x(0.4 - 0.008x), we need to solve for x when y = 0. In other words, we need to find the values of x where the equation crosses the x-axis.
To do this, we set y = 0 and solve for x:
0 = x(0.4 - 0.008x)
Next, we can factor out x from the equation:
0 = x(0.4) - x(0.008x)
0 = 0.4x - 0.008x^2
Now, we have a quadratic equation. We can solve this equation by either factoring or using the quadratic formula:
0 = 0.4x - 0.008x^2
0 = x(0.4 - 0.008x)
From here, we can see that the x intercepts occur when either x = 0 or when 0.4 - 0.008x = 0.
Solving 0.4 - 0.008x = 0, we get:
0.4 = 0.008x
x = 0.4/0.008
x ≈ 50
So, the x intercepts are x ≈ 0 and x ≈ 50.