Question

this question has two parts. first, answer part a. then, answer part b. part a suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y = 1000(2)^{0.2x}. identify the key features including the relevant domain and range of the function. select all that apply. a) the y-intercept is 1000. b) the y-intercept is 2000. c) the asymptote is y = 0. d) the asymptote is x = 0. e) there is no asymptote. f) d = {x|x ≥ 0}, r = {y|y ≥ 1000} g) d = {all real numbers}, r = {y|y ≥ 0}

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $y=1000(2)^{0.3x}$:
$y=1000(2)^{0}=1000\times1=1000$

Step2: Identify asymptote of exponential function

For $y=ab^{kx}+c$ (here $c=0$), horizontal asymptote is $y=0$.

Step3: Determine domain and range

$x$ = days, so $x\geq0$. As $x\geq0$, $2^{0.3x}\geq1$, so $y=1000(2)^{0.3x}\geq1000$.

Answer:

A) The y-intercept is 1000.
C) The asymptote is y = 0.
F) $D = \{x|x \geq 0\}, R = \{y|y \geq 1000\}$