Question

Write an exponential function in the form y = a b x y=ab x that goes through points ( 0 , 19 ) and (4,1539).

Answer 1

The function is
`y=19(3)^x`

Step-by-step explanation:

Given: An exponential function in the form
`y=ab^x` goes through points ( 0 , 19 ) and (4,1539)

To find: the function

Solution:

Put
`(x,y)=(0,19)` in
`y=ab^x`

`19=ab^0=a(1)=a`

So,
`y=19b^x`

Put
`(x,y)=(4,1539)` in
`y=ab^x`

`1539=19b^4\\(1539)/(19)=b^4\\81=b^4\\3^4=b^4\\3=b`

So,
`a=19,b=3`

The function is
`y=19(3)^x`