Answer: Choice A)
Set A is an exponential function and the values increase at a faster rate than Set B.
======================================================
Explanation:
Focus on Set A. Each time x goes up by 1, y goes up by a factor of 10. In other words, the y value is being multiplied by 10.
- 10*10 = 100
- 100*10 = 1,000
- 1,000*10 = 10,000
- 10,000*10 = 100,000
etc
This strongly implies that we're dealing with an exponential function. The equation for this function is y = 10^x.
Plug in x = 1 and you should get y = 10. Repeat for x = 2 and it should lead to y = 100. This helps confirm we have the correct function.
On the other hand, Set B deals with a linear equation which is y = 50x+950. The slope 50 is the amount we're increasing y each time x goes up by 1. If you plug x = 1 into this, you should get y = 1000. Plug in x = 2 and it leads to y = 1050, and so on.
When comparing exponential growth rates versus linear growth rates, the exponential will be faster. This is true even if you have a very small exponential growth rate. At some point, the exponential will overtake the linear. The linear growth rate is some constant value that never changes. The exponential growth rate increases over time. Think about simple interest versus compound interest and that may be a good example to go over.
