Question

question
given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

$y = 1000(1.09)^x$

answer
attempt 1 out of 2
growth % increase
submit answer

Explanation:

Step1: Identify exponential form

Exponential functions follow $y = a(1+r)^x$ (growth) or $y = a(1-r)^x$ (decay), where $a>0$.

Step2: Compare to given function

Given $y = 1000(1.09)^x$, so $1+r = 1.09$.

Step3: Solve for rate $r$

$r = 1.09 - 1 = 0.09$

Step4: Convert to percentage

$0.09 \times 100 = 9\%$

Answer:

Growth, 9% increase