Question

PLEASE HELP!!!!!!!!!!

Answer 1

Given:

The graph of an exponential function.

To find:

The function in the form of
`f(x)=ab^x`.

Solution:

The general form of an exponential function is

`f(x)=ab^x` ...(i)

From the given graph it is clear that the function passes through the points (0,4) and (1,7). It means these points will satisfy the function.

For x=0 and f(x)=4,

`4=ab^0`

`4=a(1)`

`4=a`

For x=1 and f(x)=7,

`7=ab^1`

Putting a=4, we get

`7=4(b)`

`(7)/(4)=b`

Substitute a=4 and
`b=(7)/(4)` in (i).

`f(x)=4\left((7)/(4)\right)^x`

Therefore, the required exponential function is
`f(x)=4\left((7)/(4)\right)^x`.