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
![12000=ab^0](https://tex.z-dn.net/?f=12000%3Dab%5E0)
![12000=a(1)](https://tex.z-dn.net/?f=12000%3Da%281%29)
![12000=a](https://tex.z-dn.net/?f=12000%3Da)
Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get
![3000=12000b^2](https://tex.z-dn.net/?f=3000%3D12000b%5E2)
![\dfrac{3000}{12000}=b^2](https://tex.z-dn.net/?f=%5Cdfrac%7B3000%7D%7B12000%7D%3Db%5E2)
![\dfrac{1}{4}=b^2](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%3Db%5E2)
Taking square root on both sides.
![\pm \dfrac{1}{2}=b](https://tex.z-dn.net/?f=%5Cpm%20%5Cdfrac%7B1%7D%7B2%7D%3Db)
For an exponential function b cannot be negative. So,
.
Therefore, the value of a is 12000 and the value of b is
.