1

Write an exponential function \$ y = a b^x \$ whose graph passes through Points

(1,4) and (2,16)

2

substitute the co-ordinates of the two points in equation

\$ y = a b^x \$

3

substitute the y = 4 and x = 1 and take it as equation1

\$ 4 = a b^1 \$ ⇒ equ(1)

4

substitute the y = 16 and x = 2 and take it as equation2

\$ 16 = a b^2 \$ ⇒ equ(2)

5

solve for equation 1

\$ a = 4/b \$ ⇒ equation3

6

substitute equation 3 in equation2 we get

\$ 16 = (4/b) b^2 \$

7

Simplify

\$ 16 = 4b \$

8

moving 4 for cancellation

\$ \cancel16^4/\cancel4^1 = b \$

9

After cancellation

\$ 4 = b \$

10

Substitute b = 4 in equation1

\$ 4 = a b^1\$

⇒ \$a = 4/4 = 1\$

11

So the exponential function

B = \$ y = 1(4^x) \$