Question

Given the hints for an exponential relationship between points (0,16) and (1,12), what is the decay factor 'b' in the equation y = a * b^x?

A) 0.75
B) 0.8
C) 1.25
D) 1.33

Answer 1

The decay factor 'b' in the equation y = a * b^x is (A) 0.75.

option A the correct answer.

Step-by-step explanation:

Decreasing Exponential: Since the value of y decreases from 16 to 12 as x increases from 0 to 1, we know the function represents a decreasing exponential relationship.

Decay Factor Calculation: The formula y = a * b^x shows that b, the base of the exponential term, determines the rate of decrease. In a decreasing exponential, b must be between 0 and 1.

Ratio of y-values: Observing the ratio of y-values between the two points, 16/12 = 4/3, we can see that the function decreases by a factor of 4/3 from x = 0 to x = 1.

Finding b: Since b controls the rate of decrease, it should also be equal to the ratio of y-values. Therefore, b = 4/3 = 0.75.

Therefore, based on the decreasing nature of the relationship and the ratio of y-values, the decay factor b is 0.75, making option A the correct answer.