Question

The length of a design after going through an industrial copy machine can be represented by the equation f(x)=a(b)xf(x)=a(b)x. Given that the original length is 16 inches at x=0x=0 and 12 inches at x=1x=1, what are the values of a and b?

a) a=16,b=12
b) a=16,b=0.75
c) a=12,b=0.75
d) a=12,b=16

Answer 1

The values of a and b in the equation f(x)=a(b)x can be found by substituting the given points (x,f(x)) into the equation and solving for a and b.

Step-by-step explanation:

The length of a design after going through an industrial copy machine can be represented by the equation f(x)=a(b)xf(x)=a(b)x. Given that the original length is 16 inches at x=0x=0 and 12 inches at x=1x=1, we can use these two points to solve for the values of a and b.

1. Substitute the values of x=0 and f(x)=16 into the equation and solve for a: 16 = a(b)(0)
   16 = 0
   a = 16/0
2. Substitute the values of x=1 and f(x)=12 into the equation and solve for b: 12 = a(b)(1)
   12 = a(b)
   b = 12/a

Since a cannot be divided by zero, the value of a is undefined. Therefore, the correct answer is a) a=16,b=12.