An exponential function f(x) = ab" passes through the points (0, 12000) and (2, 3000). What are the values of a and b ?

Given:

An exponential function passes through the points (0, 12000) and (2, 3000).

To find:

The values of a and b.

Solution:

We have,

     ...(i)

It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get

Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get

Taking square root on both sides.

For an exponential function b cannot be negative. So, .

Therefore, the value of a is 12000 and the value of b is .