1

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

(1,6) and (3,54)

2

substitute the co-ordinates of the two points in equation

\$ y = a b^x \$

3

substitute the y = 6 and x = 1 and take it as equation1

\$ 6 = a b^1 \$ ⇒ equ(1)

4

substitute the y = 54 and x = 3 and take it as equation2

\$ 54 = a b^3 \$ ⇒ equ(2)

5

solve for equation 1

\$ a = 6/b \$ ⇒ equation3

6

substitute equation 3 in equation2 we get

\$ 54 = (6/b) b^3 \$

7

Simplify

\$ 54 = 6(b^2) \$

8

moving 6 for cancellation

\$ \cancel54^9/\cancel6^1 = b^2 \$

9

After cancellation

\$ 9 = b^2 \$

10

simplify \$ 3^2 = b^2 \$
Hint:[b must be positive according to exponential function]

b = 3

11

Substitute b = 3 in equation1

\$ 6 = a (3^1)\$

⇒ \$a = 6/3\$ = 2

12

So the exponential function

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