If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra (all content)>Unit 7

Lesson 18: Modeling situations by combining and composing functions (Algebra 2 level)

# Modeling with function combination

Sal models the height of a tree on top of a tower, by adding the functions that model the growth of the tree and the tower separately.

## Want to join the conversation?

• 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?
• I completely agree and this video does not help with ANY of the quiz questions.
• 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?
• 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).
• I'm sure there are better resources on youtube about modeling with function combination.
• In the modeling with combined functions practice problems, when the problem states "by a factor of" something, what does that mean mathematically?
• "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.
• 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..
• "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.
• this problem is dealing with addition but how do you deal with multiplication or division?
also how do you know when to add, subtract, multiply, or divide
• Hey, so one of the questions in the exercise has something along these lines: C(t)=400t+30 is the number of batches of corn made year t, H(t)=30t+15 is the price per batch in year t, B(t) is the total profit in year t, what is B(t)?

well, you have C(t) batches and you get H(t) per batch, so B(t)= C(t) x H(t),

then to find B(t) in terms of t, perform the multiplication:

B(t) = (400t + 30)(30t + 15)
-Remember the FOIL method for multiplying out brackets,
F-first, 400t x 30t
O-outside, 400t x 15,
I-inside 30 x 30t,
L-last, 30 x 15

B(t)= 12000(t^2) + 6000t + 900t + 450
B(t) = 12000(t^2) + 6900t + 450,
which is the function for how much profit you will make!

Hope this helps a bit:):):)
If you find a question you need help with, just let me know!
• How do you know when to add, subtract, multiply or divide for the equation?
• Modelling with function combination

One college states that the number of men, M, and the number of women, W, receiving bachelor degrees t years since 1980 can be modeled by the functions

M(t) = 526 - t and W(t) = 474 + 2t

Let N be the total number of students receiving bachelor's degrees at that college t years since 1980

Write a formula for N(t) in terms of M(t) and W(t).

N(t) =

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

N(t) =

My answer for the 1st is N(t) = M(t) + W(t)

For 2nd question:

N(t) = 526 - t + 474 + 2t = 1000 + t answer//

• hi,i just have one question:
are there any more videos on this topic?
im having alot of problems doing the practice exercises