The graph of an exponential function is given. Which of the following is the correct equation of the function? y = 0.65x y = 2.4x y = 3.5x y = 0.32x

The answer is choice D

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Explanation:

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.