Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
( y = 5700(1.24)^x )
answer attempt 1 out of 2
growth (%) increase submit answer

Explanation:

Step1: Identify growth/decay form

Exponential model: $y = a(1+r)^t$ (growth) or $y = a(1-r)^t$ (decay), where $a>0$.

Step2: Compare to given function

Given $y=5700(1.24)^t$, so $1+r=1.24$.

Step3: Solve for growth rate $r$

$r = 1.24 - 1 = 0.24$

Step4: Convert to percentage

$0.24 \times 100 = 24\%$

Answer:

Growth, 24% increase