Question

The dimensions are decreasing by a constant percentage, so this is an exponential relationship. The points (0,16) and (1,12) are both part of the relationship. Because (0,16) shows the initial amount, or y-intercept, a = 16. To find the decay factor, b, find the ratio of the consecutive y-values between the points (0,16) and (1,12):

A) Determine the decay factor (b).

B) Write the exponential function representing the relationship.

Answer 1

The decay factor (b) is 0.75, obtained by dividing the y-value at x=1 by the y-value at x=0. The exponential function is y = 16(0.75)^x.

Step-by-step explanation:

To find the decay factor (b), we use the given points (0,16) and (1,12). Since the decay is by a constant percentage, we divide the y-value at x=1 by the y-value at x=0, which gives us 12/16 or 0.75. Therefore, the decay factor is 0.75.

The exponential function representing the relationship is therefore y = 16(0.75)^x, where 16 is the initial amount (y-intercept) and 0.75 is the decay factor.