Question

An industrial copy machine has the ability to reduce image dimensions by a certain percentage each time it copies. 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). put in equation f(x)=a(b)^x

Answer 1

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