Angel E.

asked • 12/17/15

Medical Maggots

1.) At one hospital doctors initially introduced 17 maggots to a patient wound. at the end of each day of treatment they introduced 9 additional maggots.

*represent the treatment with a recursive equation. Let m represent the number of days.

* determine the amount of maggots used by days 1-5

2.) Doctors at another hospital have devolved a new variety of maggots that used fewer maggots over the healing time process. at the end of day 2 there were 22 maggots in the wound. at the end of day 6 there were 14 maggots in the wound.

*Explain what the independent variable represents in this situation.
*write a linear equation that models the number of maggots in the wound and the end of each day.

3.) a third hospital in the same town has developed procedures using two varieties of maggots. in procedure 1 the doctors start with 9 maggot and introduces 2 each day. procedure 2 has 14 maggots on day 4 and 2 maggots on day 8

3a.) write and equation in slope intercept form that models the number of maggots at the end of each day for procedure 1.

3b.) write an equation in slope intercept form that model the number of maggot at the end of each day for procedure 2

3c.) estimate on what day the two procedures will have approximately the same number of maggots

*state the approximate number of maggots

Gwen B.

tutor
I'm only going to tackle one of these (because maggots). Question #2 tells us two days have passed since the patient got to this questionable “hospital.” (We're at the end of Day Two.) Let "n" equal the number of maggots removed per day & let "d" equal the number of days. (Note: The number of days doesn't depend on anything else.) n - 2d = 22 AND n - 6d = 14. To make this a one-variable equation, we can subtract one equation from the other. We'll write it as (n - 2d = 22) — (n - 6d = 14). Notice that "n" minus "n" = 0. (It no longer impacts anything, so it’s “gone.”) Let's see what happens to the variable "d." We know - 2d — (-6d) is the same as -2d + 6d, which equals 4d. Our constants are 22 and 14. Subtracting 14 from 22 gives us 8. We've got (-2d = 22) — (-6d = 14). That gets us "4d = 8." Divide both sides by 4 to see that d=2. Can we prove it? Sure. Remember, we’re at the end of Day Two. The patient must have originally had 26 maggots on him. The statements, 26 - (2)2 = 22, and 26 - (6)2 = 14 are both true. Our math problem is solved. Now, somebody PLEASE get the patient to a hospital that doesn’t have maggots (or at least doesn’t have them on staff)! Thanks.
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07/09/24

1 Expert Answer

By:

Charles W. answered • 07/11/24

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1. Total maggots would equal f(m) = 17 + 9m where m = number of days

a. Day 1 = 26 total maggots

b. Day 2 = 35 total maggots

c. Day 3 = 44 total maggots

d. Day 4 = 53 total maggots

e. Day 5 = 62 total maggots

2. Days - m Total maggots - f(m)

2 22

6 16

The independent variable in this problem would be the number of days. The linear equation that represents the new, devolved maggot scenario is f(m) = (-3/2)m +25.

3. 2 scenarios

1) f(x) = 9 +2m

2) Second Scenario

Days Maggots

4 14

2 8


3. Answers for 3

a. Y = 2x + 9

b. Y = 3x + 2

c. Same number of maggots?

d. 2x + 9 = 3x + 2

7 = x; The seventh day is the day that both procedures will have the same number of maggots if the rate of production/devolution is constant.

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