Question

Use the following graph to determine which function is best modeled on the graph.

Answer 1

We notice that (0, 2) is a point on the graph, so f(0)=2.

We check that

a)
`f(0)=2\cdot3^0=2\cdot1=2`

b)
`f(0)=3\cdot2^0=3\cdot1=3`

c)
`f(0)=2\cdot1.65^0=2\cdot1=2`

d)
`f(0)=1.65\cdot2^0=1.65\cdot1=1.65`

So, the only possible right choices are (a) and (c).


We also see that (1, 3) is on the graph, so f(1)=3.

we can check that in a, f produces 6, but in c, it produces 3.3, which is closer to what we see on the graph.

Similarly, from the graph we see that f(2) is approximately 5.

The function in a produces
`f(5)=2\cdot3^2=2\cdot9=18`, while

the function in c produces
`f(5)=2\cdot1.65^2=5.445`, which is certainly closer to what we expect from the graph.


Answer: c