Question

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

Answer 1

Answer:

f(x)=2(0.5)^x

Step-by-step explanation:

Answer 2

Answer:

$y=2(\frac{1}{2} )^x$

Step-by-step 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

$a=\frac{16}{b^{-3} } \\\\\\a=\frac{4}{b^{-1} }$

This means

$=\frac{16}{b^{-3} } =\frac{4}{b^{-1} }$

Cross multiply as;

$16b^{-1} =4b^{-3}$

Divide by 4 both sides to get

$4b^{-1} =b^{-3}$

Divide by b^-1 both sides

$\frac{4b^{-1} }{b^{-1} } =\frac{4b^{-3} }{b^{-1} } \\\\\\4=b^{-2} \\\\\\4=\frac{1}{b^2} \\\\\\b^2=\frac{1}{4} \\\\\\b=\sqrt{\frac{1}{4} } =\frac{1}{2}$

Find value of a

$4=ab^{-1} \\\\4=a*(\frac{1}{2})^{-1} \\\\\\4=a*2\\\\2=a$

Hence

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

$y=ab^x\\\\\\y=2(\frac{1}{2} )^x$