So for the first one, you'll need to write out all the factors of both 30 and 16. (30--1, 2, 3, 5, 6, 10, 15, 30) (16--1, 2, 4, 8, 16) The biggest number that goes into both 30 and 16 is 2.
For the second kne, its the same thing. (48--1, 2, 3, 4, 6, 8, 12, 16, 24, 48) (18--1, 2, 3, 6, 9, 18) The biggest number that can go into both 48 and 18 is 6.
We can rule out choice B and choice C which are y = 2.4^x and y = 3.5^x respectively. Why can we eliminate these? Because they are growth functions (the bases are larger than 1). The graph shown is a decay function. It goes downhill as you read it from left to right.
The answer is either choice A or choice D
If we plug in x = -2 into the equations for A and D, we get y = 0.65^x = 0.65^(-2) = 2.36686 y = 0.32^x = 0.32^(-2) = 9.765625
The result for choice D is much closer to what the graph is showing. The graph appears to have the point (-2,11) on the curve. So that's why choice D is the best answer.
Note: the graph is a bit small and its not entirely clear which points are on this graph other than (0,1). So this is a bit of educated guesswork.
For straight lines the constant rate of change(slope) is a constant(always the same) For every unit moved on the x-axis two more are moved on the y-axis