Question

The ordered pairs model an exponential decay function.

{(−1,30), (0,21), (1,14.7), (2,10.29)}

What is the function equation?



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f(x)=

Answer 1

The function equation is;
`y = 21(0.7)^x`

Explanation:

An exponential decay function is in the form of
`y= ab^x` ......[1]

where a≠0 is the initial value and b≠0,
`0<b<1`.

Consider any two ordered pairs to modeled the function:

(-1 , 30) and (0, 21)

Substitute these value to get a and b value ;

For (0, 21)

put x = 0 and y = 21 in [1] we get

`21 = ab^0`

or

21 = a

Similarly,

substitute (-1 , 30) we get;

`30 = ab^(-1) = (a)/(b)`

or

`30 b = a`

Substitute the value of a to solve for b;

`30 b = 21`

Divide both sides by 30 we get;

`b = (21)/(30) = 0.7`

or

b = 0.7 < 1

Value of a = 21 and b= 0.7

Substitute these values in [1] to get the required function:

`y = 21(0.7)^x`

therefore, the function equation is;
`y = 21(0.7)^x`