Question

The area in square millimeters of a wound has decreased by the same percentage every day since it began to heal. The table shows the wound's area at the end of each day.

Answer 1

Option C is correct. If c = n, we would have that b = 0.8

How to solve for the value of c

The nth term can be gotten by

nth term =
`ab^c`

This is a geometric progression

hence we would have:

a = 25, b = 16 / 20

20 / 25 = 0.8

the nth term can be written as

`25(0.8)^n`

Now if c = n, we would have that b = 0.8

Answer 2

Given the table showing the number of days since wound began to heal and area of wound in square millimeters

To determine the statement that are correct from the option provided

From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of

`(20)/(25)=(16)/(20)=(12.8)/(16)=(10.24)/(12.8)=0.8`

Suppose that an expression to represent the area of wound is

`ab^c`

The modelled expression from the table is

`\begin{gathered} a=25 \\ b=0.8 \\ c=n-1 \\ \text{Therefore, we have} \\ 25(0.8^(n-1)) \end{gathered}`

Let us use the modelled expression to verify each of the given conditions

The modelled expression can be simplified as shown below:

`\begin{gathered} 25(0.8^(n-1)) \\ \text{Note},\text{ using indices rule} \\ (a^n)/(a)=a^(n-1) \\ \text{Therefore:} \\ 0.8^(n-1)=(0.8^n)/(0.8) \end{gathered}`

Then, we have the modelled expression becomes

`25(0.8^(n-1))=25*(0.8^n)/(0.8)=(25)/(0.8)*0.8^n=31.25(0.8^n)`

From the two modelled expression we can see that

`\begin{gathered} \text{when:} \\ c=n-1,a=25,b=0.8 \\ c=n,a=31.25,b=0.8 \end{gathered}`

Then we can conclude that the two conditions that are true from the options are

If the value of c = n, the value of a is 31.25, and

If the value of c = n, the value of b is 0.8