Question

Write an exponential function y = ab^x for a graph that includes (–3, 16) and (–1, 4)

Answer 1

f(x)=2(0.5)^x

Explanation:

Answer 2

`y=2((1)/(2) )^x`

Explanation:

Given the exponential function as

`y=ab^x`

substitute both points in the equation above

point (-3,16) will be

`16=ab^(-3)`

point (-1,4) will be

`4=ab^(-1)`

make a the subject of the formula in both equations above

`a=(16)/(b^(-3) ) \\\\\\a=(4)/(b^(-1) )`

This means

`=(16)/(b^(-3) ) =(4)/(b^(-1) )`

Cross multiply as;

`16b^(-1) =4b^(-3)`

Divide by 4 both sides to get

`4b^(-1) =b^(-3)`

Divide by b^-1 both sides

`(4b^(-1) )/(b^(-1) ) =(4b^(-3) )/(b^(-1) ) \\\\\\4=b^(-2) \\\\\\4=(1)/(b^2) \\\\\\b^2=(1)/(4) \\\\\\b=\sqrt{(1)/(4) } =(1)/(2)`

Find value of a

`4=ab^(-1) \\\\4=a*((1)/(2))^(-1)  \\\\\\4=a*2\\\\2=a`

Hence

a=2 and b=1/2 thus write the equation as;

`y=ab^x\\\\\\y=2((1)/(2) )^x`