Which choice could be modeled by a linear function? А the amount of money, in an account after years earning 4% interest compounded annually the monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute B С the height, y, of a ball after bouncing times, if each bounce reaches 2/3 the previous height the amounty, of radioactive material remaining after years when decay occurs at a rate of 30% each year
all of the relations are exponential except the second one, where the rate of change is a constant number.
read up on linear functions.
Choice B, the height of a ball after bouncing times, can be modeled by a linear function.
The choice that can be modeled by a linear function is option B, which is the monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute.
To understand why this choice can be modeled by a linear function, let's break it down. A linear function is a mathematical function that has a constant rate of change. It can be represented by a straight line when plotted on a graph. In this case, the cost of using a cell phone is directly proportional to the number of minutes used.
Here's how you can determine if something can be modeled by a linear function:
1. Identify the variables involved: In this case, the variables are the monthly cost (y) and the number of minutes used (x).
2. Determine how the variables are related: The choice states that the cost of using the cell phone is 4 cents per minute. This means that for every minute used, the cost increases by 4 cents. This is a constant rate of change, which indicates a linear relationship.
3. Verify the relationship graphically: To better visualize the relationship, you can plot the data points on a graph. Let's assume you use the cell phone for different amounts of minutes and calculate the corresponding costs:
- If you use the phone for 0 minutes, the cost would be $0 (since 0 minutes multiplied by 4 cents/minute equals $0).
- If you use the phone for 10 minutes, the cost would be 10 minutes multiplied by 4 cents/minute, which equals $0.40.
- Similarly, if you use the phone for 20 minutes, the cost would be $0.80, and so on.
By plotting these data points on a graph, you will notice that they fall on a straight line. This confirms that the relationship between the cost and the minutes used can be represented by a linear function.
Therefore, the correct choice is option B, the monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute.