Question

The amount in Ebony’s bank account B d( ) is a function of the number of days d since she opened the account.

Answer 1

Answer:

1)

Domain:

$0\leq d\leq21$

Range:

$0\leq B(d)\leq 400$

2)

$B(0)=200$

On Day 0, the day Ebony opened her account, she made an initial deposit of $200.

3)

$B(12)=0$

4)

The 4th Segment.

Step-by-step explanation:

We are given the graph of the amount of money B(d) in Ebony's bank account after d days.

We know that Ebony kept her bank account open for only 3 weeks. During that time, the greatest balance was $400.

Let's answer each of the questions using the graph and the available information.

Part 1)

The domain is the span of x-values our function covers.

In this case, our domain is dealing with days.

We know that Ebony opened her account for 3 weeks, or 21 days.

Note that our domain cannot be negative because, say, Day -1 makes no sense in this context.

The maximum value of our domain is 21 Days because she only opened her account for 3 weeks.

So, our domain will be all numbers between 0 and 21 (we include the 0 because the day she opened her account is Day 0).  

So, our domain is, as a compound inequality:

$0\leq d\leq21$

The range is the span of y-values our function covers.

In this case, the range is dealing with the account balance.

We know that the greatest amount of money Ebony had in her account was $400.

Although her balance can technically be negative, this isn't shown on the graph. So, we're assuming that she always had a $0 or positive balance.

So, our range is all numbers between 0 and 400. As a compound inequality, this is:

$0\leq B(d)\leq 400$

Part 2)

We know that the greatest amount of money Ebony had in her account was $400.

So, the highest y-value is 400. We can see that this is the second segment represented by the second and third points.

B(0), the first point, seems to halfway between 0 and 400.

Therefore, it is a reasonable estimate to say that B(0) is 400/2 or $200.

This means that on Day 0, the day Ebony opened her account, she made an initial deposit of $200.

Part 3)

We are given that Ebony's balance first reached $0 on Day 12.

So, on Day 12, our d is 12.

And our B(d) is 0. Therefore, by substituting d for 12, we can write:  

$B(12)=0$

Part 4)

If the bank balance is $0, this means that the segment must be completely flat and it must lay on the x-axis.

It must lay on the x-axis because when the bank balance is $0, our y or B(d) is also 0, and this happens at the x-axis.

So, counting from the left, the segment where the balance is $0 is segment 4.

This is almost invisible, but, as we know, it's there, it's just that it's 0.

And we're done!