Question

Write an exponential function y=ab^x for a graph that includes (-4,72) and (-2,18)

Answer 1

Hello,

y=a*b^x
(-4,72)==> 72=a*b^(-4) (1)
(-2,18)==> 18=a*b^(-2) (2)

(1)/(2)==>4=b^(-2)==>b=1/2 or b=(-1/2) to exclude since b>0

b=0.5 and a*0.5²=18==>a=9/2

Y=9/2*0.5^x

Answer 2

The exponential function is
`y=(9)/(2)((1)/(2))^x`.

Explanation:

We are given,

The function
`y=ab^x` that passes through the points (-4,72) and (-2,18).

Substituting the values of x and y in the equation gives us,

`72=ab^(-4)` ................(1)

`18=ab^(-2)` ..................(2)

Dividing equation (1) by (2), we get,

`(72)/(18)=(ab^(-4))/(ab^(-2))\\\\4=b^(-2)\\\\b^2=(1)/(4)\\\\b=\pm (1)/(2)`

Since, in exponential function
`y=ab^x`, we have b > 0.

Thus,
`b=(1)/(2)`

Substituting the value in (1) gives us,

`72=a((1)/(2))^(-4)\\\\72=a* 2^4\\\\72=16a\\\\a=(9)/(2)`

Thus, the exponential function is
`y=(9)/(2)((1)/(2))^x`.