Question

Hi! I’m trying to figure out where I went wrong here. The problem is asking for the exponential function of the form “y=a•b^x” but I’m not sure how to find it

Answer 1

Given: A exponential function-

`y=a\cdot b^x`

passing through the points (1,6) and (2,9)

Required: To find out the value of a and b.

Explanation: Since the given exponential function is passing through (1,6)

`6=a\cdot b^1\text{ ..........\lparen1\rparen}`

Now the function is also passing through (2,9)

`9=a\cdot b^2\text{ ......\lparen2\rparen}`

Dividing eq 2 and eq 1 we get,

`(9)/(6)=(a\cdot b^2)/(ab^)`
`(3)/(2)=b`

Putting this value of b in eq 1,

`6=a*(3)/(2)`

This gives,

`a=4`

Final answer: The value of a=4 and b=1.5