Question

Which model is most appropriate for the data shown in the graph below?

Answer 1

Quadratic is like a parabola.
Linear is a straight line.
Exponential is like half of a parabola, but increases much faster.
A line is a line.

Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

In a quadratic function, for more that one inputs there exist same output.

The rate of change of a line and linear  function is constant.

Conditions of an exponential function:

1. The rate of change of a exponential function is not constant. The exponential function increase or decrease gradually.

2. Domain of an exponential function is all real numbers.

3. For one input there exist a unique output.

From the given graph it is clear that the function is increasing at increasing rate. The given graph satisfy all the conditions of an exponential function, so the given graph represents an exponential function.

An exponential function is defined as

$f(x)=ab^x$

The graph passing through the points (1,1) and (2,3).

$1=ab^1$                     ..... (1)

$3=ab^2$                     ..... (2)

On solving (1) and (2), we get

$a=\frac{1}{3},b=3$

$f(x)=\frac{1}{3}(3)^x$

Therefore the correct option is c.