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

$7=4(b)$

$\dfrac{7}{4}=b$

Substitute a=4 and $b=\dfrac{7}{4}$ in (i).

$f(x)=4\left(\dfrac{7}{4}\right)^x$

Therefore, the required exponential function is $f(x)=4\left(\dfrac{7}{4}\right)^x$.