Question

Find the formula for an exponential function that passes through the two points given. (x, y) = (0, 4) and (x, y) = (3, 32)

Answer 1

Given:

The exponential function passes through two points (0,4) and (3,32).

To find:

The formula for the exponential function.

Solution:

The general form of an exponential function is

$y=ab^x$          ...(i)

where, a is initial value and b is growth factor.

The exponential function passes through two points (0,4) and (3,32). It means the function must be satisfy by these points.

Putting x=0 and y=4 in (i), we get

$4=ab^0$

$4=a(1)$

$4=a$

Putting a=4, x=3 and y=32 in (ii), we get

$32=4b^3$

Divide both sides by 4.

$8=b^3$

Taking cube root on both sides.

$2=b$

Putting a=4 and b=2 in (i), we get

$y=4(2)^x$

Therefore, the required formula for the exponential function is $y=4(2)^x$.