Quadratic Functions

[JDRhoads]

I don't know if this is considered algebra for sure. If its in the wrong place I apologize.

On one of my assignments I was told to fill out this question:

"A pool is treated with a chemical to reduce the number of algae. The number of algae in the pool t days after the treatment can be approximated by the function:
'A(t) = 40t^2 - 400t + 500.' Create a table from 0 days through 16 days then graph the function using good graphing practices."

They provided me with a table with the x column filled out 1 - 16. I inputted the equation into my calculator and filled out the rest of the table as follows:

x | y

0 | 500
1 | 140
2 | -140
3 | -340
4 | -460
5 | -500
6 | -460
7 | -340
8 | -140
9 | 140
10 | 500
11 | 940
12 | 1460
13 | 2060
14 | 2740
15 | 3500
16 | 4340

My first question is "How can they're be a negative number of algae? Technically this makes no sense, is the table proper?"

The next part of the assignment asks "How many days after treatment will the pool have the least number of algae? Show how you got your answer."

The second part I arranged the equation as such:

0 = 40(t)^2 - 400(t) + 500
-500 = 40(t)^2 -400(t)

I may have slowed down in my ability to perform this kind of math but I do not remember how to proceed. Any help would be appreciated thanks!!

 

[Deleted member 4993]

I don't know if this is considered algebra for sure. If its in the wrong place I apologize.

On one of my assignments I was told to fill out this question:

"A pool is treated with a chemical to reduce the number of algae. The number of algae in the pool t days after the treatment can be approximated by the function:
'A(t) = 40t^2 - 400t + 500.' Create a table from 0 days through 16 days then graph the function using good graphing practices."

They provided me with a table with the x column filled out 1 - 16. I inputted the equation into my calculator and filled out the rest of the table as follows:

x | y

0 | 500
1 | 140
2 | -140
3 | -340
4 | -460
5 | -500
6 | -460
7 | -340
8 | -140
9 | 140
10 | 500
11 | 940
12 | 1460
13 | 2060
14 | 2740
15 | 3500
16 | 4340

My first question is "How can they're be a negative number of algae? Technically this makes no sense, is the table proper?"

The next part of the assignment asks "How many days after treatment will the pool have the least number of algae? Show how you got your answer."

The second part I arranged the equation as such:

0 = 40(t)^2 - 400(t) + 500
-500 = 40(t)^2 -400(t)

I may have slowed down in my ability to perform this kind of math but I do not remember how to proceed. Any help would be appreciated thanks!!

You are correct - negative number of living creature will not make sense. If I were to do this problem, I would make all the negative entries equal to zero (with an asterisk).

As for the next part:

40(t)^2 - 400(t) + 500 = 0

2t² - 20t + 25 = 0

This is a quadratic equation. For a quick refresher to solving these equations - go to

http://www.purplemath.com/modules/quadform.htm

After reading that may be you won't have any more doubts!!

 

[JeffM]

I don't know if this is considered algebra for sure. If its in the wrong place I apologize.

On one of my assignments I was told to fill out this question:

"A pool is treated with a chemical to reduce the number of algae. The number of algae in the pool t days after the treatment can be approximated by the function:
'A(t) = 40t^2 - 400t + 500.' Create a table from 0 days through 16 days then graph the function using good graphing practices."

They provided me with a table with the x column filled out 1 - 16. I inputted the equation into my calculator and filled out the rest of the table as follows:

x | y

0 | 500
1 | 140
2 | -140
3 | -340
4 | -460
5 | -500
6 | -460
7 | -340
8 | -140
9 | 140
10 | 500
11 | 940
12 | 1460
13 | 2060
14 | 2740
15 | 3500
16 | 4340

My first question is "How can they're be a negative number of algae? Technically this makes no sense, is the table proper?"

The next part of the assignment asks "How many days after treatment will the pool have the least number of algae? Show how you got your answer."

The second part I arranged the equation as such:

0 = 40(t)^2 - 400(t) + 500
-500 = 40(t)^2 -400(t)

I may have slowed down in my ability to perform this kind of math but I do not remember how to proceed. Any help would be appreciated thanks!!

The most probable explanation is that there is a typo in the approximating equation.

For example, \(\displaystyle 40t^3 - 400t + 500\) gives no negative values for non-negative t. Of course, other typos are possible.

If there is no typo, then the approximating equation is unreliable for the days when it gives a negative result.

 

[JDRhoads]

Thanks. I got 1.46 days and 8.53 days which matches the graph on the x axis's. I wrote

"Since it is illogical to believe there is a negative number of algae in the pool, it can be assumed that between 1.46 days until 8.53 days the algae count was 0."

Would you accept this answer? This teacher is a pain in the *** and criticizes everything! =(

 

[mmm4444bot]

Thanks. I got 1.46 days and 8.53 days which matches the graph on the x axis's. I wrote

"Since it is illogical to believe there is a negative number of algae in the pool, it can be assumed that between 1.46 days until 8.53 days the algae count was 0."

Would you accept this answer? This teacher is a pain in the *** and criticizes everything! =(

Yes, I would accept that statement as correct (for the posted model). But, are you required to make such a statement?

Your original post does not seem to indicate that you're required to find actual t-intercept values. I read the instructions as requiring only a table of values and a graph.

Did you post only a portion of the exercise?

By the way, between the t-intercepts, does your graph show the parabola below the axis OR did you draw that part of the graph along the t-axis (to indicate A=0 in that interval)?

Also, if values are required to be stated, has your instructor been accepting decimal approximations for word-problem solutions, in the past?

For example, the exact value of approximated 1.46 is 5-(5/2)*sqrt(2)

I always wonder about this, when instructors fail to specific some number of digits to which solutions should be rounded. (Maybe they want the exact values.)

You could change the phrase "between 1.46 days until 8.53 days" to "between t=1.46 and t=8.53 days".

Cheers :cool: