Answer:
a = 16
b = 3/4
Step-by-step explanation:
Given that the function to represent the
industrial copy machine that has the ability to reduce image dimensions by a certain percentage each time it copies is f(x)=a(b)^x
Where
F(x) = length of the paper
X = number of times
If a design began with a length of 16 inches, represented by the point (0,16). After going through the copy machine once, the length is 12, represented by the point (1,12).
To put in equation f(x)=a(b)^x, we will substitute for f(x) and x in the equation
At point ( 0, 16 )
16 = a(b)^0
Anything at exponential zero is equal to one. Therefore,
16 = a(1)
a = 16
At point ( 1, 12 )
12 = a (b)^1
12 = ab
Since a = 16, substitute into the equation above.
12 = 16b
b = 12/16
b = 3/4
