Question

Write an exponential function in the form y=ab^x that goes through points (0,12) and (3,6144)

Answer 1

Given:

An exponential function goes through points (0,12) and (3,6144).

To find:

The exponential function.

Solution:

The general exponential function is:

$y=ab^x$           ...(i)

The function goes through point (0,12). Substituting $x=0,y=12$, we get

$12=ab^0$

$12=a$

The function goes through point (3,6144). Substituting $a=12, x=3,y=6144$ in the general exponential function, we get

$6144=12b^3$

$\dfrac{6144}{12}=b^3$

$512=b^3$

$512^{\frac{1}{3}}=b$

$8=b$

Putting $a=12,b=8$ in (i), we get

$y=12(8)^x$

Therefore, the required exponential function is $y=12(8)^x$.