Question

Given the exponential function y = 5600(0.82)^x, determine whether the change represents growth or decay, and calculate the percentage rate of increase or decrease.

A) Growth; 18%
B) Decay; 18%
C) Growth; 82%
D) Decay; 82%

Answer 1

The exponential function y = 5600(0.82)^x represents exponential decay, not growth, with a decay rate of 18%.

Step-by-step explanation:

The exponential function provided in the question is y = 5600(0.82)^x. To determine if the function represents exponential growth or decay, we need to look at the base of the exponent (0.82 in this case). Because the base of the exponent is less than 1, the function represents exponential decay, not growth.

To calculate the percentage rate of decrease, subtract the base from 1 (1 - 0.82 = 0.18) and then convert it to a percentage by multiplying by 100. This gives us a rate of decrease of 18%. The correct answer is B) Decay; 18%.