Question

Now, that you have a deeper understanding of the topic, I believe that you are ready to solve the problems below.

Mission Possible

1. The volume V of air remaining in an inflated balloon can be modeled by the function V = 1,000(0.85) where x represents the number of days that have passed since inflating the balloon. What is the reasonable domain for the situation? Explain.

2. The function f(x)=65,000(1.5) can be modeled the population of a city for x, the number of years that have passed since 2010. What inequality represents the reasonable range of the function based on the situation? Explain.

Answer 1

1.

$$V=1000(0.85)^x$$

Since $x$ represents the number of days that have passed since inflating the balloon, we assume that $x\geq0.$

Since $V$ represents the volume of air remaining in an inflated balloon, then $V\to0$ as $x\to \infin.$

Therefore the  reasonable domain for the situation is $[0, \infin).$

2.

$$f(x)=65000(1.5)^x$$

Since $x$ represents the number of years that have passed since 2010, we assume that $x\geq0.$

$$f(0)=65000(1.5)^0=65000$$

Since $1.5>1$ the function $f(x)$ increases for $x\geq0,$ $f(x)\to \infin$ as $x\to \infin.$

Therefore the  reasonable range of the function based on the situation is $[65000, \infin).$