Question

The graph below could be the graph of which exponential function?

Answer 1

Your answer is B F(x) * (0.5)^x

Answer 2

The graph could be a graph of the function:

Option: B B.
`F(x)=2\cdot (0.5)^x`

Explanation:

We know that for any exponential function of the type:

`f(x)=ab^x`

if b>1 then it represent a exponential growth

and if 0<b<1 then it represent a exponential decay.

Clearly from the graph given to us we could observe that it is a graph of a exponential decay.

Hence 0<b<1

Now we will check for each of the given options:

A)

`F(x)=2\cdot (1.6)^x`

Now as b=1.6>1

So, this function will represent a exponential growth.

Hence, option: A is incorrect.

C)

`F(x)=2\cdot (7)^x`

Now as b=7>1

So, this function will represent a exponential growth.

Hence, option: C is incorrect.

D)

`F(x)=2^x`

Now as b=2>1

So, this function will represent a exponential growth.

Hence, option: D is incorrect.

B)

`F(x)=2\cdot (0.5)^x`

Now as b=0.5<1 and also 0.5>0

So, this function will represent a exponential decay

Hence, option: B is correct.