select each situation in which one quantity at a constant rate in relation to another quantity.
A. Brad drives 45 miles per hour.
B. Frank earns 3% interest on his savings account
C. Steve doubles the amount of water he drinks every week.
D. Dan earns $12 for every lawn he takes.
E. Charlie runs 3 miles every day.
My answers.
B and D
You can't choose both B and D!
B grows by a constant 3% rate, or a factor of 1.03
D grows by a constant difference of just 12
Both cannot express the same model.
To determine which situations involve one quantity changing at a constant rate in relation to another quantity, we need to consider the given information for each scenario:
A. Brad drives 45 miles per hour.
Here, we are given a fixed rate of 45 miles per hour. However, because it only relates to Brad's driving speed, there is no other quantity involved that changes at a constant rate with respect to this rate. Therefore, this situation does not fit the criteria.
B. Frank earns 3% interest on his savings account.
In this case, Frank's earnings are tied to a fixed percentage (3%) of his savings account balance. As his savings account balance increases or decreases, the amount of interest earned will change at a constant rate proportional to the account balance. Hence, this situation fits the criteria as one quantity changes relative to another at a constant rate.
C. Steve doubles the amount of water he drinks every week.
This situation does not involve a constant rate of change between two quantities. Steve's water consumption is not directly linked to any specific rate, but rather it doubles every week. As a result, the change in quantity is not consistent, so this scenario does not meet the criteria.
D. Dan earns $12 for every lawn he takes.
Here, Dan's earnings are directly tied to the number of lawns he takes. Regardless of the total number of lawns, his earnings remain constant at $12 per lawn. Since the change in earnings is directly proportional to the change in the number of lawns at a constant rate, this qualifies as a situation where one quantity changes at a constant rate in relation to another.
E. Charlie runs 3 miles every day.
Charlie's daily running distance is fixed at 3 miles per day. While this represents a constant amount, there is no second quantity involved that changes relative to this rate. Hence, this scenario does not fit the criteria.
In conclusion, situations B (Frank earns 3% interest on his savings account) and D (Dan earns $12 for every lawn he takes) involve one quantity changing at a constant rate in relation to another quantity.