# Is the weighted average of growth rates equal to the growth rate of a weighted average?

More formally, is the following statement true? Let $$\alpha$$ be between 0 and 1.

$$$$\alpha\frac{(A_t - A_{t-1})}{A_{t-1}}\ + (1-\alpha)\frac{(B_t - B_{t-1})}{B_{t-1}}= \frac{(\alpha A_t + (1-\alpha)B_t)-(\alpha A_{t-1} + (1-\alpha)B_{t-1})}{(\alpha A_{t-1} + (1-\alpha)B_{t-1})}$$$$

If it is not true, is it possible to determine how much they differ by?

• To investigate whether this is true, something you could do is just plug in some numbers and see what happens. – Minus One-Twelfth Jun 6 '19 at 12:31
• Yeah I see it now, thank you for reminding me! – yonderkens Jun 6 '19 at 12:37