1

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

(2,3) and (5,81)

2

substitute the co-ordinates of the two points in equation

\$ y = a b^x \$

3

substitute the y = 3 and x = 2 and take it as equation1

\$ 3 = a b^2 \$ ⇒ equ(1)

4

substitute the y = 81 and x = 5 and take it as equation2

\$ 81 = a b^5 \$ ⇒ equ(2)

5

solve for equation 1

\$ a = 3/ b^2 \$ ⇒ equation3

6

substitute equation 3 in equation2 we get

\$ 81 = (3/ b^2) b^5 \$

7

Simplify

\$ 81 = 3(b^3) \$

8

moving 3 for cancellation

\$ \cancel81^27/\cancel3^1 = b^3 \$

9

After cancellation

\$ 27 = b^3 \$

10

simplify \$ 3^3 = b^3 \$
Hint:[b must be positive according to exponential function]

b = 3

11

Substitute b = 3 in equation1

\$ 3 = a (3^2)\$

⇒ \$a = 3/9 = 1/3\$

12

So the exponential function

C = \$ y = (1/3)(3^x) \$