Question

On Day 16 (in Segment 5), Ebony deposited $100 into her account. On each day after Day 16 (Segment 6) Ebony made a deposit, and those deposits were equal to each other.
(a) Explain how you can determine, just by looking at the graph, whether the amounts she deposited after Day 16 were each less than, equal to, or greater than $100.

(b) Use the graph to estimate B(21) in hundreds. Explain how you determined this estimate. Then, show how you can estimate the amount of money Ebony deposited into her account each day after Day 16.

Answer 1

Answer:

A)

Less than $100

B)

$B(21)=300$

For each day after Day 16, Ebony deposited $40.

Step-by-step explanation:

We know that on Day 16 she deposited $100 into her account.

And each day after Day 16, she made a deposit and each deposit were equal to each other.

So, let's answer each of the questions using the available information.

Part A)

Notice that the 5th Segment starts and ends with the 5th to the 6th Point. The 6th Point represents the 16th Day, where B(16)=100.

We want to know whether or not each of her deposits after Day 16 were less than, equal to, or greater than $100.

We can immediately conclude that it must be less than $100 because we can see that the slope of the 6th Segment is less steep than the slope of the 5th Segment.

Since it is less steep, this means that the unit rate of change from each day after Day 16 is less than the unit change on Day 16, which is $100/day.

So, the each of the deposits made after Day 16 is less than $100.

Part B)

We want to estimate B(21) in hundreds.

Remember that Ebony's maximum balance is $400.

Also, recall that the first point is $200.

B(21), the 7th Point, seems to be between the 2nd/3rd Point and the 1st Point.

So, it is reasonable to say that at the 21st Day, her account balance was (200+400)/2=600/2=$300.

We know that at Day 16, her account balance was $100. So, we have the point (16, 100).

And at Day 21, her account balance is $300. So, (21, 300).

Since each deposit after Day 16 is the same, it has a constant rate of change. So, we can use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let (16, 100) be (x₁, y₁) and let (21, 300) be (x₂, y₂). Substitute them into the slope formula. This yields:

$m=\frac{300-100}{21-16}$

Subtract and divide. So:

$m=\frac{\ 200}{5\text{ days}}=\ 40\text{/day}$

So, for each day after Day 16, Ebony deposited $40.

And we're done!