Which choice could be modeled by a linear function?
A. The amount of money, y, in an account after x years earning 4% interest compounded annually
B. The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute
C. the height, y, of a ball after bouncing x times, if each bounce reaches ⅔ the previous height
D. the amount, y, of radioactive material remaining after x years when decay occurs at a rate of 30% each year
The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute
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the mostly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute
A. The amount of money, y, in an account after x years earning 4% interest compounded annually.
Why did the banker bring a ladder to the bank? To reach a higher interest rate!
To determine which choice could be modeled by a linear function, we need to understand the characteristics of a linear function. A linear function is a function that can be represented by a straight line on a graph. It has the form y = mx + b, where m is the slope and b is the y-intercept.
Now, let's analyze the given choices:
A. The amount of money, y, in an account after x years earning 4% interest compounded annually:
This choice involves exponential growth due to the compounding interest. Therefore, it cannot be modeled by a linear function.
B. The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute:
This choice can be modeled by a linear function. The cost increases linearly with the number of minutes used. The slope, in this case, would be 4 cents per minute.
C. The height, y, of a ball after bouncing x times, if each bounce reaches ⅔ the previous height:
This choice involves geometric progression, where the height decreases by a factor of 2/3 with each bounce. Therefore, it cannot be modeled by a linear function.
D. The amount, y, of radioactive material remaining after x years when decay occurs at a rate of 30% each year:
This choice involves exponential decay due to the 30% decay rate. Again, it cannot be modeled by a linear function.
Therefore, the only choice that could be modeled by a linear function is B. The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute.