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

User Tzali
by
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2 Answers

2 votes

Answer:

f(x)=2(0.5)^x

Explanation:

User MJoy
by
8.2k points
4 votes

Answer:


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

User Henry Daehnke
by
8.7k points

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