Question

Write an exponential function y= ab^x for a graph that includes (1,15) and (0,6)

Answer 1

basically you write an exponential function for y=ab^x for a graph that includes (1,15) and (0,6)
then using (0,6) you get: 6 = ab^0
and using (1,15) you get 15 = ab^1

Equations:
a = 6
ab = 15
So, b = 15/6 = 5/2
Equation:
y = 6(5/2)^x

Answer 2

The required exponential function is
`y=6((5)/(2))^x`.

Explanation:

The general exponential function is

`y=ab^x`

It is given that graph includes (1,15) and (0,6). It means the equation must be satisfied by these points.

`15=ab^1` .... (1)

`6=ab^0`

`6=a`

The value of a is 6. Put this value in equation (1).

`15=(6)b`

Divide both sides by 6.

`(15)/(6)=b`

`(5)/(2)=b`

The value of b is
`(5)/(2)`.

Put a=6 and
`b=(5)/(2)` in the general exponential function.

`y=6((5)/(2))^x`

Therefore the required exponential function is
`y=6((5)/(2))^x`.