Tiffany has been dieting for 6 months. After 1 month Tiffany lost a total of 8 pounds. After 6 months, she lost a total of 25 pounds. How do you find the average rate of change of pounds per month?

We want to calculate Tiffany's average rate of change of weight over a time period. To do this, we'll be employing the following formula:

#DeltaW = (W_f - W_i)/(Deltat)#

..where #W# represents the amount of weight Tiffany has lost at any given time.

We know that she'd lost 8 pounds after 1 month, and 25 after 6. Therefore, we have an initial weight loss, final weight loss, and a time interval. All we need to do, therefore, is plug it all in:

#DeltaW = (25 - 8)/(6-1)#

#color(blue)(= 3.4)# pounds lost per month

Notice my vocabulary in that final answer: I make sure I specify that I'm saying that she's lost that much weight per month. It's important to make this distinction, since the answer 3.4 pounds per month can very easily be interpreted as a gain in weight, which is not what we're saying. So, make sure you're meticulous about that.

This video I made explains the concepts of average rates of change, and relates them to the study of derivatives, which you'll likely be doing soon:

Hope that helps :)