1

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

(1,2) and (3,32)

2

substitute the co-ordinates of the two points in equation

\$ y = a b^x \$

3

substitute the y = 2 and x = 1 and take it as equation1

\$ 2 = a b^1 \$

4

substitute the y = 32 and x = 3 and take it as equation2

\$ 32 = a b^3 \$

5

solve for equation 1

\$ a = 2/b \$ ⇒ equation3

6

substitute equation 3 in eqauation2 we get

\$ 32 = (2/b) b^3 \$

7

Simplify

\$ 32 = 2(b^2) \$

8

moving 2 for cancellation

\$ \cancel32^16/\cancel2^1 = b^2 \$

9

After cancellation

\$ 16 = b^2 \$

10

simplify \$ 4^2 = b^2 \$
Hint:[b must be positive according to exponential function]

b = 4

11

Substitute b = 4 in equation1

\$ 2 = a b^1\$

⇒ \$a = 2/4 = 1/2\$

12

So the exponential function

A = \$ y = (1/2)(4^x) \$