given the following exponential function, identify whether the change represents growth or decay, and…

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\n\n$y = 3800(0.97)^{x}$

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\n\n$y = 3800(0.97)^{x}$

Answer

Answer:

Decay, (3%) decrease

Explanation:

Step1: Recall the exponential function form

The general form of an exponential function is (y = a(1 + r)^x) (growth) or (y=a(1 - r)^x) (decay), where (a) is the initial value and (r) is the rate of change.

Step2: Compare with the given function

Given (y = 3800(0.97)^x), we can rewrite (0.97) as (1-0.03).

Step3: Determine growth/decay and rate

Since (0.97<1), it represents decay. The rate (r = 0.03), so the percentage rate of decrease is (3%) (because (r\times100%=0.03\times 100% = 3%)).