Question 1

I don't know when your suppose to multiply them or add them or subtract them or divide them. I keep getting all of the practice questions wrong and its honestly frustrating me. could you please help me. when do I do which?

Accepted Answer

I completely agree and this video does not help with ANY of the quiz questions.

Question 2

There should be more videos that explain how to do this. 
Also, when I was doing the activity for this video, the question about Haruka's ponch factory doesn't make sense.  Can you explain what the prompt is saying?

Accepted Answer

In order for a company to determine the total profit(the amount of money it gets to keep after expenses are covered), it must subtract its total expenses(costs in the form of wages, land taxes, production costs,etc.) from its revenue(money made from the distribution of a product/service). Thus, Profit=Revenue-Costs.

In this example, the total revenue depends on both how many ponchos are sold and the sales price of each poncho. Since each poncho sells for $18, the money made from the sale of one poncho is 18; the amount made from the sale of two ponchos is 2*18=36; the amount made from the sale of three ponchos is 3*18;; and so on. So in general, the total revenue for selling n ponchos is 18*n=18n.

The problem describes the total profit as a linear function of n(the number of ponchos sold). I say "linear" because for every additional poncho sold, the profit increases by $17, starting with a profit of $12 for one poncho sold. This means that for n=1, P(1)=12, P(2)=12+17=29, P(3)=17+29=46, .....and so on. Thus, profit function is best modeled by the equation P(n)=17(n-1)+12=17n-17+12=17n-5. You could derive this using the point slope formula of a line.

With both the revenue and profit functions, you should be able to solve for the cost function on your own using P(n)=R(n)-C(n).

Question 3

Okay this is 4th question for this problem and its baffles me. here it is.

The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10,000(1.1)^t. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t)=450 + 40t.

Let D be the average number of students per classroom in Emor's school system t years from 2000.

Write a formula for D(t) in terms of S(t) and C(t).

D(t) =?

Write a formula for D(t) in terms of t.

D(t) =

My answer from D(t) in terms of S(t) and C(t) is = [2000 + S(t)]/[2000 + C(t)]

then D(t) in terms of t is  =[2000 + 10,000(1.1)^t]/[2000 + 450 + 40t]

= [2000 + 10,000(1.1)^t]/[2450 + 40t]

Please verify my answer if I'm correct.. Please provide correct answer if I'm wrong. I made the last 3 questions correct, and don't want to fail this last question which really makes me stump..

Accepted Answer

"t" is always defined as the number of year from 2000.  So, you don't need to add the 2000's into your function.
The average students / classroom = S(t)/C(t)
D(t) = [10,000(1.1)^t] / (450 + 40t)

Hope this helps.

Question 4

In the modeling with combined functions practice problems, when the problem states "by a factor of" something, what does that mean mathematically?

Accepted Answer

"by a factor of" means multiplication. It can also mean division if something is _reduced_ "by a factor of." Look out for when it's combined with the phrase "for each," though, because then you're looking at exponents. Here are some examples.

My electricity usage increases by a factor of four in the summertime. In the winter, I spend $15 / month on electricity. So in the summer months, I spend $60 / month. 15 x 4 = 60.

By bringing my lunch to work, I have reduced my spending on food by a factor of six. I used to spend $240 / month on lunch. Now I spend only $40 / month on lunch. 240 / 6 = 40. _Or_, 240 x 1/6 = 40.

Every time I drop a cookie on the floor, the number of ants in my house increases. _For each_ cookie I drop, the number of ants increases by a factor of three. I started with six ants, and then I dropped two cookies. Now there are 54 ants. 6 x 3 x 3 = 54, or 6 x 3² = 54.

To look at that last one another way, since it's a little confusing, you can break it apart to consider the cookies separately. I had six ants, and I dropped a cookie. 6 x 3 = 18. Now I have 18 ants, and I dropped another cookie. 18 x 3 = 54.

Question 5

in the practice question. when I try to use hint to understand. I saw this:
(2^t)⋅(1.5^t) == (2 ⋅ 1.5)^t
can someone tall me please which rule of exponent power is this? sorry I forget it and I want to research and study it.
Thank you.

Accepted Answer

You should know:  (a*b)^n = a^n * b^n
The example above just uses the property in reverse (from right to left).  
Does that make sense?

Algebra (all content)

Course: Algebra (all content) > Unit 7

Modeling with function combination

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