1

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

(0,3) and (3,24)

2

substitute the co-ordinates of the two points in equation

\$ y = a b^x \$

3

substitute the y = 3 and x = 0 and take it as equation1

\$ 3 = a b^0 \$ ⇒ equ(1)

4

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

\$ 24 = a b^3 \$ ⇒ equ(2)

5

substitute \$ b^0 = 1\$

\$ 3 = a(1)\$ ⇒ a = 3

6

substitute a = 3 in equation2 we get

\$ 24 = 3(b^3) \$

7

moving 3 for cancellation

\$ \cancel24^8/\cancel3^1 = b^3 \$

8

Simplify

\$ 8 = b^3 \$

9

simplify

\$ 2^3 = b^3 \$

10

After cancellation

\$ 2 = b \$

11

So the exponential function

D = \$ y = 3(2^x) \$