Analyzing Functions in Context

a

We can make a table by choosing arbitrary $p -$ values and calculate their corresponding $A -$ values by using the given function.

$p$	$0.08 p$	$A = 0.08 p$	$(p, A)$
$0$	$0.08 \cdot 0$	$0$	$(0, 0)$
$0.5$	$0.08 \cdot 0.5$	$0.04$	$(0.5, 0.04)$
$1$	$0.08 \cdot 1$	$0.08$	$(1, 0.08)$
$1.5$	$0.08 \cdot 1.5$	$0.12$	$(1.5, 0.12)$
$2$	$0.08 \cdot 2$	$0.16$	$(2, 0.16)$
$3$	$0.08 \cdot 3$	$0.24$	$(3, 0.24)$
$5$	$0.08 \cdot 5$	$0.4$	$(5, 0.4)$

b

Let's plot the points we have calculated in Part A in a coordinate plane and connect them with a straight line.

c

To find the number of people who attended the concert in Philadelphia, where $1.5$ million people live, we look up the corresponding $A$ -value to $p = 1.5$ using the graph.

The number of people that saw the concert in Philadelphia is about $0.1$ million.

d

The domain of the function is all whole numbers. $v \geq 0$ This is because the population in a city cannot be negative and it can not be a fraction. But would it make sense for a city have a population of $0 ?$ Well, there are ghost towns that have a population of $0 .$ Therefore, we should include $0$ even though it is unlikely that SR-71 would give a show in one.

Analyzing Functions in Context 1.12 - Solution