Put the items in order from least steep to steepest rate of change.
Susie has $200 in her savings account,She plans to spend $5 per week until she has a total of $100. Jim's puppy weighed 4 pounds when it was born.It gained 3 pounds per month until it was 9 months old. F(t) = -10x +5 G(x) = 15x + 1
F(t) = -10x +5 (has a constant rate of change of -10)
Susie has $200 in her savings account,She plans to spend $5 per week until she has a total of $100. (has a rate of change of -5/week)
Jim's puppy weighed 4 pounds when it was born.It gained 3 pounds per month until it was 9 months old. (has a rate of change of 3 pounds/month)
G(x) = 15x + 1 (has a constant rate of change of 15)
Order from least steep to steepest rate of change:
Susie's savings account, Jim's puppy weight, F(t), G(x).
To put the items in order from least steep to steepest rate of change, let's examine each scenario:
1. F(t) = -10x + 5: This is a linear function with a negative slope of -10. The rate of change is constant, and the slope represents how much the function value changes for each unit change in t. Since the slope is negative, the function value decreases as t increases.
2. Susie's savings account: Susie plans to spend $5 per week until she has a total of $100. In this case, the rate of change is a constant -5 dollars per week. The rate of change is negative because Susie is spending money, so her savings decrease over time.
3. Jim's puppy's weight: The puppy weighed 4 pounds when it was born and gained 3 pounds per month until it was 9 months old. The rate of change here is a constant positive 3 pounds per month. As time (months) increases, the puppy's weight increases by 3 pounds each month.
4. G(x) = 15x + 1: This is another linear function, but with a positive slope of 15. Similar to F(t), the rate of change is constant, and the slope represents the change in the function value for each unit change in x. Since the slope is positive, the function value increases as x increases.
Based on the information above, we can order the rate of change from least steep to steepest as follows:
1. Susie's savings account (-$5 per week)
2. Jim's puppy's weight (+3 pounds per month)
3. G(x) = 15x + 1 (+15 per unit change in x)
4. F(t) = -10x + 5 (-10 per unit change in t)