Answer:
The function equation is; [tex]y = 21(0.7)^x[/tex]
Step-by-step explanation:
An exponential decay function is in the form of [tex]y= ab^x[/tex] ......[1]
where a≠0 is the initial value and b≠0, [tex]0<b<1[/tex].
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
[tex]21 = ab^0[/tex]
or
21 = a
Similarly,
substitute (-1 , 30) we get;
[tex]30 = ab^{-1} = \frac{a}{b}[/tex]
or
[tex]30 b = a[/tex]
Substitute the value of a to solve for b;
[tex]30 b = 21[/tex]
Divide both sides by 30 we get;
[tex]b = \frac{21}{30} = 0.7[/tex]
or
b = 0.7 < 1
Value of a = 21 and b= 0.7
Substitute these values in [1] to get the required function:
[tex]y = 21(0.7)^x[/tex]
therefore, the function equation is; [tex]y = 21(0.7)^x[/tex]
